A brief overview of the theories of superconductivity and the problems of high-temperature superconductivity are analyzed. School encyclopedia

In 1911, the Dutch scientist Kamenlingh Onnes discovered that the resistivity of pure mercury at a temperature TO dropped sharply to zero. The electric current in such a conductor remained unchanged for as long as desired. This phenomenon is called superconductivity.

In Fig. 3.8. shows the temperature dependence of the resistivity of the superconductor. The temperature at which the metal transitions to the superconducting state is called the critical temperature.

Currently, superconductivity has been discovered in 22 chemical elements ( Pb, Zn, Al etc.) and more than 100 metal alloys (for example Au 2 Bi).

For a long time, the superconducting state of various metals and compounds could be obtained only at very low temperatures, achievable with the help of liquid helium. By the beginning of 1986, the maximum observed value of the critical temperature was 23 K. In 1986-1987. A number of high-temperature superconductors with a critical temperature of the order of 100 K and then higher were discovered. This was an important leap, since the “nitrogen limit” was overcome: this temperature is achieved using liquid nitrogen. Unlike helium, liquid nitrogen is produced on an industrial scale.

All high-temperature superconductors discovered so far belong to the group of metal oxide ceramics (compounds of the La-Ba-Cu-O, Y-Ba-Cu-O). The study of already discovered and the search for new high-temperature superconductors is carried out very intensively in a number of countries (including our country).

Let's consider the basic properties of superconductors.

The superconducting state can be destroyed by a magnetic field. It makes no difference whether this field is external to the conductor or whether it is created by the current flowing through the conductor itself. A magnetic field of strength , which at a given temperature causes a transition of a substance from a superconducting state to a normal one, is called critical. The critical field depends on temperature T in law

, (3.4.1)

Where H 0–critical field at T = 0 K.

This dependence is shown graphically in Fig. 3.9. At external magnetic field values H, large 2/3 H C, an intermediate state arises in a superconductor, which is characterized by the simultaneous existence of two regions in the normal and superconducting states.

One of the properties of a superconductor is the complete expulsion of the magnetic field from the internal volume when it is introduced into an external field with intensity . This phenomenon is called Meissner effect. The pushing out of a magnetic field by a superconductor is shown in Fig. 3.10.

The resulting magnetic induction in the superconductor will be zero.

It follows that the relative magnetic permeability of the superconductor is also zero, and the magnetic susceptibility is negative and equal (in absolute value) to one. That is, a superconductor is not only an ideal conductor, but also an ideal diamagnetic.

Physically, the Meissner effect is due to the fact that a superconductor placed in a weak magnetic field has a thick surface layer L » 10 ¸100 nm, circular undamped currents are induced, which compensate for the external applied field. Parameter L is called the depth of penetration of the magnetic field into the superconductor.

The transition to the superconducting state is accompanied by a decrease in thermal conductivity. This indicates that free electrons, responsible for heat transfer in metals, cease to interact with the lattice and participate in heat transfer. When a superconductor transitions to the normal state, the increase in entropy is about 10 -3 R(Here R– universal gas constant). The small entropy difference between the two states suggests that although the superconducting state is more ordered, it probably only contains a small fraction of the electrons.

The microscopic theory of superconductivity was developed in 1957 by N.N. Bogolyubov, J. Bardin, A. Cooper and J. Schrieffer. Let us briefly consider the essence of this theory.

The free electrons of the metal form an electron gas that obeys Fermi-Dirac statistics. Repulsive forces act between electrons, which are significantly weakened by the presence of a field of positive ions located at the nodes of the crystal lattice. The participation of the lattice can lead to the appearance between electrons, in addition to Coulomb repulsion forces, also of mutual attraction forces. Under certain conditions, attractive forces can prevail over repulsive forces. If one of the electrons is close to an ion, then it causes a displacement of this ion from its equilibrium position - an elementary excitation of the crystal lattice occurs. When the lattice transitions to the ground unexcited state, a quantum of thermal energy (sound frequency) is emitted - phonon, which is absorbed by another electron. As a result, attraction occurs between two electrons through the exchange of phonons, that is, the so-called Cooper couple.

The electrons forming a Cooper pair have antiparallel spins, the total (total) spin of such a pair is zero, and therefore it is a boson. The Pauli principle does not apply to bosons, so the number of Bose particles in the same quantum state is not limited.

At low temperatures, bosons accumulate in the ground state, from which it is difficult to transfer them to an excited state. From the point of view of band theory, the ground state level is located below the Fermi level and is separated from other levels by an energy gap (gap) wide DE s(Fig. 3.11). Energy gap width at T = 0 K turned out to be approximately 3.5 kT C.

The minimum portion of energy that a Cooper pair can receive at the main level is equal to DE S. At low temperatures, it cannot receive such energy from the lattice. Therefore, electrons move in the metal without losing energy and without braking. As the temperature increases, the width of the energy gap decreases, and electron pairs are broken. At a temperature T C the width of the energy gap becomes zero, and the superconducting state disappears.

Distance between electrons in a Cooper pair

Where v F - electron speed at the Fermi level.

The assessment shows that δ ≈10 -6 m; this means that the electrons are separated from each other at a distance of about 10 4 lattice periods ( d ~10 -10 m). All conduction electrons at represent a bound collective consisting of Cooper pairs, extending over the entire volume of the crystal. A feature of such a collective of electrons in a superconductor is the impossibility of exchanging energy between electrons and the lattice in small portions, less than the binding energy of a Cooper pair.

When such a group of electrons moves, electron waves are not scattered by thermal vibrations of the lattice or impurities; they go around lattice sites or impurity atoms without changing their energy. This means no electrical resistance.

The properties of superconductors make them promising materials for practical use in electrical engineering and energy. Currently, losses due to Joule heat in the supply wires are estimated at 30-40%, that is, more than a third of all energy produced is wasted in vain - on “heating” the Universe. If you transmit electricity through superconducting wires with zero resistance, then there will be no such losses at all. Superconductors can be used to create high-efficiency electric motors and generators.

With the help of superconducting coils and solenoids, huge magnetic fields up to 16 MA/m are already being created. Such fields are required to solve the problem of controlled thermonuclear fusion to contain hot plasma, to develop magnetic levitation transport, magnetic bearings, microwave detectors and other devices.

Superconductivity - the property of some materials to have strictly zero electrical resistance when they reach a temperature below a certain value (critical temperature). Several dozen pure elements, alloys and ceramics are known that transform into a superconducting state. Superconductivity is a quantum phenomenon. It is also characterized by the Meissner effect, which consists in the complete displacement of the magnetic field from the volume of the superconductor. The existence of this effect shows that superconductivity cannot be described simply as ideal conductivity in the classical sense.

Opening in 1986-1993. a number of high-temperature superconductors (HTSC) has pushed back the temperature limit of superconductivity far and has made it possible to practically use superconducting materials not only at the temperature of liquid helium (4.2 K), but also at the boiling point of liquid nitrogen (77 K), a much cheaper cryogenic liquid.

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History of discovery

The basis for the discovery of the phenomenon of superconductivity was the development of technologies for cooling materials to ultra-low temperatures. In 1877, French engineer Louis Cayette and Swiss physicist Raoul Pictet independently cooled oxygen to a liquid state. In 1883, Zygmunt Wróblewski and Karol Olszewski liquefied nitrogen. In 1898, James Dewar managed to obtain liquid hydrogen.

In 1893, the Dutch physicist Heike Kamerlingh Onnes began to study the problem of ultra-low temperatures. He managed to create the best cryogenic laboratory in the world, in which he obtained liquid helium on July 10, 1908. Later he managed to bring its temperature to 1 degree Kelvin. Kamerlingh Onnes used liquid helium to study the properties of metals, in particular to measure the dependence of their electrical resistance on temperature. According to the classical theories that existed at that time, the resistance should gradually fall with decreasing temperature, but there was also an opinion that at too low temperatures the electrons would practically stop and stop conducting current altogether. Experiments conducted by Kamerlingh Onnes with his assistants Cornelis Dorsman and Gilles Holst initially confirmed the conclusion about a smooth decrease in resistance. However, on April 8, 1911, he unexpectedly discovered that at 3 degrees Kelvin (about −270 °C), the electrical resistance of mercury is practically zero. The next experiment, carried out on May 11, showed that a sharp jump in resistance to zero occurs at a temperature of about 4.2 K (later, more accurate measurements showed that this temperature is 4.15 K). This effect was completely unexpected and could not be explained by the then existing theories.

In 1912, two more metals were discovered that go into a superconducting state at low temperatures: lead and tin. In January 1914, it was shown that superconductivity is destroyed by a strong magnetic field. In 1919, it was discovered that thallium and uranium are also superconductors.

Zero resistance is not the only distinguishing feature of superconductivity. One of the main differences between superconductors and ideal conductors is the Meissner effect, discovered by Walter Meissner and Robert Ochsenfeld in 1933.

The first theoretical explanation of superconductivity was given in 1935 by Fritz and Heinz London. A more general theory was constructed in 1950 by L. D. Landau and V. L. Ginzburg. It has become widespread and is known as the Ginzburg-Landau theory. However, these theories were phenomenological in nature and did not reveal the detailed mechanisms of superconductivity. Superconductivity was first explained at the microscopic level in 1957 in the work of American physicists John Bardeen, Leon Cooper and John Schrieffer. The central element of their theory, called the BCS theory, is the so-called Cooper pairs of electrons.

It was later discovered that superconductors are divided into two large families: type I superconductors (which, in particular, include mercury) and type II (which are usually alloys of different metals). The work of L.V. Shubnikov in the 1930s and A.A. Abrikosov in the 1950s played a significant role in the discovery of type II superconductivity.

Of great importance for practical applications in high-power electromagnets was the discovery in the 1950s of superconductors that could withstand strong magnetic fields and carry high current densities. Thus, in 1960, under the leadership of J. Künzler, the Nb3Sn material was discovered, a wire from which is capable of passing a current with a density of up to 100 kA/cm² at a temperature of 4.2 K, being in a magnetic field of 8.8 T.

In 1962, the English physicist Brian Josephson discovered the effect that received his name.

In 1986, Karl Müller and Georg Bednorz discovered a new type of superconductors, called high-temperature superconductors. In early 1987, it was shown that compounds of lanthanum, strontium, copper and oxygen (La-Sr-Cu-O) experience a jump in conductivity to almost zero at a temperature of 36 K. In early March 1987, a superconductor was obtained for the first time at temperatures above boiling of liquid nitrogen (77.4 K): it was discovered that the compound of yttrium, barium, copper and oxygen (Y-Ba-Cu-O) has this property. As of January 1, 2006, the record belongs to the ceramic compound Hg-Ba-Ca-Cu-O(F), discovered in 2003, the critical temperature for which is 138 K. Moreover, at a pressure of 400 kbar, the same compound is a superconductor at temperatures up to 166 K.

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Phase transition to the superconducting state

The temperature range of transition to the superconducting state for pure samples does not exceed thousandths of a Kelvin and therefore a certain value of Tc - the temperature of transition to the superconducting state - makes sense. This value is called the critical transition temperature. The width of the transition interval depends on the heterogeneity of the metal, primarily on the presence of impurities and internal stresses. The currently known temperatures Tc vary from 0.0005 K for magnesium (Mg) to 23.2 K for the intermetallic compound of niobium and germanium (Nb3Ge, in film) and 39 K for magnesium diboride (MgB2) for low-temperature superconductors (Tc below 77 K , boiling point of liquid nitrogen), to approximately 135 K for mercury-containing high-temperature superconductors. Currently, the HgBa2Ca2Cu3O8+d (Hg−1223) phase has the highest known value of the critical temperature - 135 K, and at an external pressure of 350 thousand atmospheres the transition temperature increases to 164 K, which is only 19 K lower than the minimum temperature recorded under natural conditions at surface of the Earth. Thus, superconductors in their development have gone from metallic mercury (4.15 K) to mercury-containing high-temperature superconductors (164 K).

The transition of a substance to the superconducting state is accompanied by a change in its thermal properties. However, this change depends on the type of superconductors in question. Thus, for type I superconductors in the absence of a magnetic field at the transition temperature Tc, the heat of transition (absorption or release) goes to zero, and therefore suffers a jump in heat capacity, which is characteristic of a type II phase transition. This temperature dependence of the heat capacity of the electronic subsystem of a superconductor indicates the presence of an energy gap in the distribution of electrons between the ground state of the superconductor and the level of elementary excitations. When the transition from the superconducting state to the normal state is carried out by changing the applied magnetic field, then heat must be absorbed (for example, if the sample is thermally insulated, then its temperature decreases). And this corresponds to a phase transition of the 1st order. For type II superconductors, the transition from the superconducting to the normal state under any conditions will be a phase transition of type II.

Meissner effect

An even more important property of a superconductor than zero electrical resistance is the so-called Meissner effect, which consists in the superconductor pushing out a magnetic flux rotB = 0. From this experimental observation, it is concluded that there are continuous currents inside the superconductor, which create an internal magnetic field that is opposite to the external applied magnetic field and compensates for it.

A sufficiently strong magnetic field at a given temperature destroys the superconducting state of the substance. A magnetic field with intensity Hc, which at a given temperature causes a transition of a substance from a superconducting state to a normal state, is called a critical field. As the temperature of the superconductor decreases, the value of Hc increases. The dependence of the critical field on temperature is described with good accuracy by the expression

where Hc0 is the critical field at zero temperature. Superconductivity also disappears when an electric current with a density greater than the critical one is passed through the superconductor, since it creates a magnetic field greater than the critical one.

London moment

The rotating superconductor generates a magnetic field precisely aligned with the axis of rotation, the resulting magnetic moment is called the “London moment.” It was used, in particular, in the Gravity Probe B scientific satellite, where the magnetic fields of four superconducting gyroscopes were measured to determine their axes of rotation. Since the rotors of gyroscopes were almost perfectly smooth spheres, using the London moment was one of the few ways to determine their axis of rotation.

Applications of Superconductivity

Significant progress has been made in obtaining high-temperature superconductivity. Based on metal ceramics, for example, the composition YBa2Cu3Ox, substances have been obtained for which the temperature Tc of transition to the superconducting state exceeds 77 K (the temperature of nitrogen liquefaction).

The phenomenon of superconductivity is used to produce strong magnetic fields, since there is no heat loss when strong currents pass through a superconductor, creating strong magnetic fields. However, due to the fact that the magnetic field destroys the state of superconductivity, so-called so-called magnetic fields are used to obtain strong magnetic fields. Type II superconductors, in which the coexistence of superconductivity and a magnetic field is possible. In such superconductors, a magnetic field causes the appearance of thin threads of normal metal that penetrate the sample, each of which carries a magnetic flux quantum. The substance between the threads remains superconducting. Since there is no full Meissner effect in a type II superconductor, superconductivity exists up to much higher values of the magnetic field Hc2.
There are photon detectors based on superconductors. Some use the presence of a critical current, they also use the Josephson effect, Andreev reflection, etc. Thus, there are superconducting single-photon detectors (SSPD) for recording single photons in the IR range, which have a number of advantages over detectors of a similar range (PMTs, etc.) using other registration methods.
Vortexes in type II superconductors can be used as memory cells. Some magnetic solitons have already found similar applications. There are also more complex two- and three-dimensional magnetic solitons, reminiscent of vortices in liquids, only the role of current lines in them is played by the lines along which elementary magnets (domains) are lined up.

Electrons in metals
The discovery of the isotope effect meant that superconductivity was likely caused by interactions between conduction electrons and atoms in the crystal lattice. To figure out how this leads to superconductivity, we need to look at the structure of the metal. Like all crystalline solids, metals consist of positively charged atoms arranged in space in a strict order. The order in which the atoms are placed can be compared to a repeating pattern on wallpaper, but the pattern must repeat in three dimensions. Conduction electrons move among the atoms of the crystal at speeds ranging from 0.01 to 0.001 the speed of light; their movement is electric current.

Introduction

Chapter 1 Discovery of the phenomenon of superconductivity

1.2 Superconducting substances

1.3 Meissner effect

1.4 Isotopic effect

Chapter 2 Theory of superconductivity

2.1 BCS theory

2.4 Formation of electron pairs

2.5 Effective interaction between electrons due to phonons

2.6 Canonical Bogolyubov transformation

2.7 Intermediate state

2.8 Type II superconductors

2.9 Thermodynamics of superconductivity

2.10 Tunnel contact and Josephson effect

2.11 Magnetic flux quantization (macroscopic effect)

2.12 Knight shift

2.13 High temperature superconductivity

Chapter 3. Application of superconductivity in science and technology

3.1 Superconducting magnets

3.2 Superconducting electronics

3.3 Superconductivity and energetics

3.4 Magnetic suspensions and bearings

Conclusion

Bibliography

Introduction

For most metals and alloys, at a temperature of about a few degrees Kelvin, the resistance abruptly goes to zero. This phenomenon, called superconductivity, was first discovered in 1911 by Kamerlingh Onnes. Substances with this phenomenon are called superconductors. In 1957, J. Bardeen, L. Cooper, J. Schrieffer developed a microscopic theory of superconductivity, which made it possible to fundamentally understand this phenomenon. The BCS theory explained the basic facts in the field of superconductivity (the absence of resistance, the dependence of Tc on the mass of the isotope, infinite conductivity (E = 0), the Meissner effect (B = 0), the exponential dependence of the electronic heat capacity near T = 0, etc.). A number of theoretical conclusions show good quantitative agreement with experiment. Many issues still need to be developed (distribution of superconducting metals in the periodic system, dependence of Tc on the composition and structure of superconducting compounds, the possibility of obtaining superconductors with the highest possible transition temperature, etc.). The successes of experimental and theoretical research have provided a real opportunity to begin work on mastering this physical phenomenon. For almost 100 years, developments have been going on in this area, new superconducting materials are being discovered, and the search for high-temperature superconductors is underway. In recent years, especially after the creation of the theory of superconductivity, technical superconductivity has been intensively developing.

Relevance. Today, superconductivity is one of the most studied areas of physics, a phenomenon that opens up serious prospects for engineering practice. Devices based on the phenomenon of superconductivity have become widespread; neither modern electronics, nor medicine, nor astronautics can do without them.

Target. Consider in more detail the phenomenon of superconductivity, its properties, practical application, study the BCS theory, and also find out the prospects for the development of this field of physics.

1) Find out what superconductivity is, the reasons for its occurrence and the conditions for the possible transition of a substance from a normal state to a superconducting state.

2) Explain the reasons influencing the destruction of the superconducting state.

3) Reveal the properties and applications of superconductors.

An object. The object of this course work is the phenomenon of superconductivity, superconductors.

Item. The subject is the properties of superconductors and their applications.

Practical use. The phenomenon of superconductivity is used to produce strong magnetic fields; superconductors are used in the creation of computers, for the construction of modulators, rectifiers, switches, persistors and persistrons, and measuring instruments.

Research methods. Analysis of scientific literature.

Chapter 1. Discovery of the phenomenon of superconductivity

1.1 First experimental facts

In 1911, in Leiden, the Dutch physicist H. Kamerlingh Onnes first observed the phenomenon of superconductivity. This problem was studied earlier; experiments showed that with decreasing temperature, the resistance of metals decreased. One of his first studies in the field of low temperatures was the study of the dependence of electrical resistance on temperature during an experiment with a mercury circuit. Mercury was then considered the purest metal that could be obtained by distillation. Studying the temperature variation of the electrical resistance of Hg, he discovered that at temperatures below 4.2 0 K, mercury practically loses its resistance. For this experiment, he used an apparatus (Fig. 1), which consisted of seven U-shaped vessels with a cross-section of 0.005 mm 2, connected inverted. This form of vessels was needed for free compression and expansion of mercury without breaking the continuity of the mercury thread. At points 1 and 2, current was supplied through tubes 3 and 4; at points 5 and 6, the voltage drop in sections of the mercury circuit was measured.

Figure 2 shows the results of his experiments with mercury. It should be noted that the temperature range in which the resistance decreased to zero is extremely narrow.

Rice. 2. Dependence of the resistance of platinum and mercury on temperature.

The graph shows that at a temperature of 4.2 0 K the electrical resistance of mercury suddenly disappeared. This state of a conductor in which its electrical resistance is zero is called superconductivity, and substances in this state are called superconductors. The transition of a substance to the superconducting state occurs in a very narrow temperature range (hundredths of a degree) and therefore it is believed that the transition occurs at a certain temperature Tc, called the critical temperature of the transition of the substance to the superconducting state.

Superconductivity can be observed experimentally in two ways:

1) by including a superconductor link in the general electrical circuit through which current flows. At the moment of transition to the superconducting state, the potential difference at the ends of this link becomes zero;

2) by placing a ring of superconductor in a magnetic field perpendicular to it. Having then cooled the ring below Tc, turn off the field. As a result, a continuous electric current is induced in the ring. The current circulates in such a ring indefinitely.

Kamerling - Onnes demonstrated this by transporting a superconducting ring with current flowing through it from Leiden to Cambridge. In a number of experiments, the absence of current attenuation in the superconducting ring was observed for about a year. In 1959, Collins reported that he observed no decrease in current for two and a half years. .

Experiments have shown that if a current is created in a closed loop from superconductors, then this current continues to circulate without an EMF source. Foucault currents in superconductors persist for a very long time and do not fade due to the lack of Joule heat (currents up to 300A continue to flow for many hours in a row). A study of the passage of current through a number of different conductors showed that the resistance of the contacts between superconductors is also zero. A distinctive property of superconductivity is the absence of the Hall phenomenon. While in ordinary conductors, under the influence of a magnetic field, the current in the metal is shifted, in superconductors this phenomenon is absent. The current in a superconductor is, as it were, fixed in its place.

Superconductivity disappears under the influence of the following factors:

1) increase in temperature;

As the temperature rises to a certain Tk, noticeable ohmic resistance almost suddenly appears. The transition from superconductivity to conductivity is steeper and more noticeable the more homogeneous the sample is (the steepest transition is observed in single crystals).

2) the action of a sufficiently strong magnetic field;

The transition from the superconducting state to the normal state can be accomplished by increasing the magnetic field at a temperature below the critical Tc. The minimum field Bc in which superconductivity is destroyed is called the critical magnetic field. The dependence of the critical field on temperature is described by the empirical formula:

where B 0 is the critical field extrapolated to absolute zero temperature. For some substances there appears to be a dependence on T to the first degree. If we begin to increase the external field strength, then at its critical value, superconductivity will collapse. The closer we get to the critical temperature point, the lower the external magnetic field strength must be to destroy the effect of superconductivity, and vice versa, at a temperature equal to absolute zero, the strength must be maximum in relation to other cases to achieve the same effect. This relationship is illustrated by the following graph (Fig. 3).

If we begin to increase the external field strength, then at its critical value, superconductivity will collapse. The closer we get to the critical temperature point, the lower the external magnetic field strength must be to destroy the effect of superconductivity, and vice versa, at a temperature equal to absolute zero, the strength must be maximum in relation to other cases to achieve the same effect. When a magnetic field acts on a superconductor, a special type of hysteresis is observed, namely if, by increasing the magnetic field, superconductivity is destroyed at (H - field strength, H to - increased field strength):

then, with a decrease in the field intensity, superconductivity will reappear under the field, varies from sample to sample and is usually 10% Hc.

3) a sufficiently high current density in the sample;

An increase in current strength also leads to the disappearance of superconductivity, that is, Tk decreases. The lower the temperature, the higher the maximum current strength ik at which superconductivity gives way to ordinary conductivity.

4) change in external pressure;

A change in external pressure p causes a shift in Tk and a change in the magnetic field strength, which destroys superconductivity.

1.2 Superconducting substances

Later it was found that not only mercury, but also other metals and alloys, the electrical resistance becomes zero when sufficiently cooled.

Niobium (9.22 0 K) has the highest critical temperature among pure substances, and iridium has the lowest (0.14 0 K). The critical temperature depends not only on the chemical composition of the substance, but also on the structure of the crystal itself. For example, gray tin is a semiconductor, and white tin is a metal that passes into the superconducting state at a temperature of 3.72 0 K. Two crystalline modifications of lanthanum (b-La and b-La) have different critical temperatures of transition to the superconducting state (for b -La T k =4.8 0 K, c-La T k =5.95 0 K). Therefore, superconductivity is not a property of individual atoms, but a collective effect associated with the structure of the entire sample.

Good conductors (silver, gold and copper) do not have this property, but many other substances that are very poor conductors under normal conditions do, on the contrary, do. It came as a complete surprise to the researchers and further complicated the explanation of this phenomenon. The bulk of superconductors are not pure substances, but their alloys and compounds. Moreover, an alloy of two non-superconducting substances can have superconducting properties. There are type I and type II superconductors.

Type I superconductors are pure metals; there are more than 20 of them in total. Among them there are no metals that are good conductors at room temperature, but, on the contrary, metals that have relatively poor conductivity at room temperature (mercury, lead, titanium, etc.).

Superconductors of the second type are chemical compounds and alloys, and these do not necessarily have to be compounds or alloys of metals, which in their pure form are superconductors of the first type. For example, the compounds MoN, WC, CuS are type II superconductors, although Mo, W, Cu and especially N, C and S are not superconductors. The number of type II superconductors is several hundred and continues to increase. .

1.3 Meissner effect

In 1933, Meissner and Ochsenfeld established that behind the phenomenon of superconductivity lies something more than ideal conductivity, that is, zero resistivity. They discovered that a magnetic field is pushed out of the superconductor regardless of whether the field is created by an external source or by a current flowing through the superconductor itself (Fig. 4). It turned out that the magnetic field does not penetrate into the thickness of the superconducting sample.

Figure 4. Pushing out a flux of magnetic induction from a superconductor.

At temperatures higher than the critical temperature of transition to the superconducting state, in a sample placed in an external magnetic field, as in any metal, the magnetic field induction inside is different from zero. If, without turning off the external magnetic field, the temperature is gradually reduced, then at the moment of transition to the superconducting state, the magnetic field will be pushed out of the sample and the magnetic field induction inside will become zero (B = 0). This effect was called the Meissner effect.

As is known, metals, with the exception of ferromagnets, have zero magnetic induction in the absence of an external magnetic field. This is due to the fact that the magnetic fields of elementary currents, which are always present in matter, are mutually compensated due to the complete randomness of their location.

Placed in an external magnetic field, they become magnetized, i.e. a magnetic field is “induced” inside. The total magnetic field of a substance introduced into an external magnetic field is characterized by a magnetic induction equal to the vector sum of the induction of the external and the induction of the internal magnetic fields, i.e. . In this case, the total magnetic field can be either greater or less than the magnetic field.

In order to determine the degree of participation of a substance in the creation of a magnetic field by induction, the ratio of induction values is found. The coefficient µ is called the magnetic permeability of a substance. Substances in which, when an external magnetic field is applied, the resulting internal field is added to the external one (µ > 1) are called paramagnets. At a coefficient >1, the external field in the sample decreases.

In diamagnetic substances (<1) наблюдается ослабление приложенного поля. В сверхпроводниках В=0, что соответствует нулевой магнитной проницаемости. В поверхностном слое металла возникает стационарный электрический ток, собственное магнитное поле которого противоположно приложенному полю и компенсирует его, что в результате и приводит к нулевому значению индукции в толще образца.

The existence of stationary superconducting currents is revealed in the following experiment: if a superconducting sphere is placed above a metal superconducting ring, then a continuous superconducting current is induced on its surface. Its occurrence leads to a diamagnetic effect and the emergence of repulsive forces between the ring and the sphere, as a result of which the sphere will float above the ring. The depth of field penetration into the sample is one of the main characteristics of a superconductor. Typically the penetration depth is approximately 100...400E. With increasing temperature, the depth of penetration of the magnetic field increases according to the law:

The simplest estimate of the depth of penetration of a magnetic field into a superconductor was given by the brothers Fritz and Hans London. Let us present this estimate. We will assume that we are dealing with fields that slowly change over time. Since superconductors are not ferromagnetic, we can neglect the difference between and and write the fundamental equations of electrodynamics in the form

Moreover, we will also neglect the difference between the partial and total derivatives with respect to time. Assuming that currents are created by the movement of only superconducting electrons, we will further write where is the concentration of such electrons. After differentiation with respect to time we get: The acceleration of the electron can be found from the equation if the effect of the magnetic field is neglected. Then

where the designation is introduced

Having differentiated the first equation (4) with respect to, excluding the quantities and from equations (4) and (5), we obtain

This equation is satisfied, but such a solution is not consistent with the Meissner effect, since there must be inside the superconductor. The extra solution was obtained because during the derivation the operation of differentiation with respect to time was used twice. To automatically eliminate this solution, the Londons introduced the hypothesis that in the last equation the derivative should be replaced by the vector itself. This gives

To determine the depth of penetration of the magnetic field into the superconductor, let us assume that the latter is limited by a plane on one side of it. Let's direct the axis inside the superconductor normal to its boundary. Let the magnetic field be parallel to the axis, so. Then

And equation (8) gives

The solution to this equation, which vanishes at, has the form

The integration constant gives the field on the surface of the superconductor. Over the length, the magnetic field decreases by a factor. The value is taken as a measure of the depth of penetration of the field into the metal.

To obtain a numerical estimate, we assume that for each metal atom there is one superconducting electron, assuming cm -3. then using formula (6) we find cm, which in order of magnitude coincides with the values obtained by direct measurements.

The surface layer of a superconductor has special properties associated with the nonzero magnetic field strength in it. These properties have a very significant impact on the production of superconductors with high critical fields.

A situation arises when surface currents, often called shielding currents, prevent the applied field from penetrating the magnetic flux into the sample. If the magnetic flux inside a substance in an external field is zero, then it is said to exhibit ideal diamagnetism. When the applied field density decreases to zero, the sample remains in its non-magnetized state. In another case, when a magnetic field is applied to the sample above the transition temperature, the final picture will change noticeably. For most metals (except ferromagnets), the relative magnetic permeability is close to unity. Therefore, the magnetic flux density inside the sample is almost equal to the flux density of the applied field. The disappearance of electrical resistance after cooling does not affect magnetization, and the distribution of magnetic flux does not change. If we now reduce the applied field to zero, then the magnetic flux density inside the superconductor cannot change; undamped currents appear on the surface of the sample, maintaining the magnetic flux inside. As a result, the sample remains magnetized all the time. Thus, the magnetization of an ideal conductor depends on the sequence of changes in external conditions.

The effect of pushing a magnetic field out of a superconductor can be explained on the basis of ideas about magnetization. If screening currents, which completely compensate the external magnetic field, impart a magnetic moment m to the sample, then the magnetization M is expressed by the relation:

where V is the volume of the sample. We can say that shielding currents lead to the appearance of magnetization corresponding to the magnetization of an ideal ferromagnet with a magnetic susceptibility equal to minus one.

The Meissner effect and the phenomenon of superconductivity are closely related and are a consequence of a general pattern, which was established by the theory of superconductivity, created more than half a century after the discovery of the phenomenon.

1.4 Isotopic effect

In 1950, E. Maxwell and C. Reynolds discovered the isotope effect, which was of great importance for the creation of the modern theory of superconductivity. A study of several superconducting isotopes of mercury showed that there is a relationship between the critical temperature of transition to the superconducting state and the mass of the isotopes. When the mass M of the isotope changed from 199.5 to 203.4, the critical temperature changed from 4.185 to 4.14 K. For this superconducting chemical element, a formula was established that is justified with sufficient accuracy:

where const has a specific value for each element.

The mass of an isotope is a characteristic of the crystal lattice, since the main contribution to it is made by metal ions. Mass determines many lattice properties. It is known that the frequency of lattice vibrations is related to mass:

Superconductivity, which is a property of the electronic system of a metal, turns out to be associated, due to the discovery of the isotope effect, with the state of the crystal lattice. Consequently, the occurrence of the superconductivity effect is due to the interaction of electrons with the metal lattice. This interaction is responsible for the resistance of the metal in its normal state. Under certain conditions, it should lead to the disappearance of resistance, that is, to the effect of superconductivity.

1.5 Prerequisites for the creation of the theory of superconductivity

The first theory that quite successfully described the properties of superconductors was the theory of F. London and G. London, proposed in 1935. The Londons in their theory were based on a two-fluid model of a superconductor. It was believed that when in a superconductor there are “superconducting” electrons with a concentration and “normal” electrons with a concentration, where is the total conductivity concentration). The density of superconducting electrons decreases with increasing and goes to zero at. When it tends to the density of all electrons. A current of superconducting electrons flows through the sample without resistance.

London, in addition to Maxwell's equations, obtained equations for the electromagnetic field in such a superconductor, from which its basic properties followed: the absence of resistance to direct current and ideal diamagnetism. However, due to the fact that the Londons' theory was phenomenological, it did not answer the main question of what “superconducting” electrons are. In addition, it had a number of other shortcomings, which were eliminated by V.L. Ginzburg and L.D. Landau.

In the Ginzburg-Landau theory, quantum mechanics was used to describe the properties of superconductors. In this theory, the entire set of superconducting electrons was described by a wave function of one spatial coordinate. Generally speaking, the wave function of electrons in a solid is a function of coordinates. By introducing the function, the coherent, consistent behavior of all superconducting electrons was established. Indeed, if all electrons behave in exactly the same way, in a consistent manner, then to describe their behavior, the same wave function is sufficient as to describe the behavior of one electron, i.e. functions of one variable.

Despite the fact that the Ginzburg-Landau theory, which was further developed in the works of A.A. Abrikosov, described many properties of superconductors, it could not provide an understanding of the phenomenon of superconductivity at the microscopic level.

This chapter discusses the discovery of the phenomenon of superconductivity, the first experimental facts, the first theories, as well as some properties of superconductors.

Analyzing the above, the following conclusions can be drawn:

1) This state of a conductor in which its electrical resistance is zero is called superconductivity, and substances in this state are called superconductors.

2) Foucault currents in superconductors persist for a very long time and do not fade due to the lack of Joule heat (currents up to 300A continue to flow for many hours in a row).

3) Superconductivity disappears under the influence of the following factors: an increase in temperature, the action of a sufficiently strong magnetic field, a sufficiently high current density in the sample, a change in external pressure.

4) The magnetic field is pushed out of the superconductor regardless of how this field is created - an external source or a current flowing through the superconductor itself.

5) There is a connection between the critical temperature of transition to the superconducting state and the mass of isotopes, which is called the isotope effect.

6) The isotopic effect indicated that lattice vibrations are involved in the creation of superconductivity.

Chapter 2. Theory of superconductivity

2.1 BCS theory

In 1957, Bardeen, Cooper and Schrieffer constructed a consistent theory of the superconducting state of matter (BCS theory). Long before Landau, the theory of superfluidity of helium II was created. It turned out that superfluidity is a macroscopic quantum effect. However, the transfer of Landau's theory to the phenomenon of superconductivity was hindered by the fact that helium atoms, having zero spin, obey Bose-Einstein statistics. Electrons, having half spin, obey the Pauli principle and Fermi-Dirac statistics. For such particles, Bose-Einstein condensation, which is necessary for the occurrence of superfluidity, is impossible. Scientists have suggested that electrons are grouped into pairs that have zero spin and behave like Bose particles. Regardless of them, in 1958 N.N. Bogolyubov developed a more advanced version of the theory of superconductivity.

The BCS theory refers to an idealized model in which the structural features of the metal are so far completely discarded. The metal is considered as a potential box filled with an electron gas that obeys Fermi statistics. Coulomb repulsion forces act between individual electrons, largely weakened by the field of the atomic cores. The isotope effect in superconductivity indicates the presence of interaction of electrons with thermal vibrations of the lattice (with phonons).

An electron moving in a metal deforms and polarizes the crystal lattice of the sample by electrical forces. The displacement of the lattice ions caused by this is reflected in the state of the other electron, since it now finds itself in the field of a polarized lattice, which has somewhat changed its periodic structure. Thus, the crystal lattice acts as an intermediate medium in electronic interactions, since with its help electrons realize attraction to each other. At high temperatures, sufficiently intense thermal motion pushes particles away from each other, effectively reducing the force of attraction. But at low temperatures, attractive forces play a very important role.

Two electrons repel each other if they are in empty space. In the environment, the force of their interaction is equal to:

where e is the dielectric constant of the medium. If the environment is such that<0, то одноименные заряды, в том числе и электроны, будут притягиваться. Кристаллическая решетка некоторых веществ является той средой, в которой выполняется это условие, а значит при определенных температурах возможно возникновение эффекта сверхпроводимости. Таким образом, эффект взаимного притяжения электронов не противоречит законам физики, так как происходим в некоторой среде.

Let's consider a metal at T = 0 0 K. Its crystal lattice undergoes “zero” vibrations, the existence of which is associated with the quantum-mechanical uncertainty relation. An electron moving in a crystal disrupts the vibration mode and transfers the lattice to an excited state. The return transition to the previous energy level is accompanied by the emission of energy, captured by another electron and exciting it. The excitation of the crystal lattice is described by sound quanta - phonons, therefore the process described above can be represented as the emission of a phonon by one electron and its absorption by another electron, while the crystal lattice plays an intermediate role as a transmitter. The exchange of phonons determines their mutual attraction.

At low temperatures, this attraction for a number of substances prevails over the Coulomb repulsive forces of electrons. In this case, the electronic system turns into a connected collective, and in order to excite it, the expenditure of some finite energy is required. The energy spectrum of the electronic system in this case will not be continuous - the excited state is separated from the ground state by an energy gap.

It has now been established that the normal state of a metal differs from the superconducting state in the nature of the energy spectrum of electrons near the Fermi surface. In the normal state at low temperatures, electronic excitation corresponds to the transition of an electron from an initially occupied state to (<к F) под поверхностью Ферми в свободное состояние к (>to F) above the Fermi surface. The energy required to excite such an electron-hole pair in the case of a spherical Fermi surface is equal to

Since k and k 1 can lie quite close to the Fermi surface, then.

The electronic system in a superconductor can be represented as consisting of bound pairs of electrons (Cooper pairs), and excitation as the breaking of the pair. The size of the electron pair is approximately ~10 -4 cm, the size of the lattice period is 10 -8 cm. That is, the electrons in the pair are located at a huge distance.

The most characteristic property of a metal in a superconducting state is that the excitation energy of a pair always exceeds a certain certain value 2D, which is called the pairing energy. In other words, there is a gap in the excitation energy spectrum on the low-energy side. For example, for the metals Hg, Pb, V, Nb, the value 2D corresponds to thermal energy at temperatures of 18 0 K, 29 0 K, 18 0 K and 30 0 K.

The magnitude of the pairing energy is measured directly experimentally: when studying the absorption of electromagnetic radiation, only radiation with a frequency ђш = 2Д is absorbed, when studying the exponential change in sound attenuation, etc.

If there is a gap in the energy spectrum, quantum transitions of the system will not always be possible. The electronic system will not be excited at low speeds, therefore, the movement of electrons will occur without friction, which means there is no resistance. At a certain critical current, the electronic system will be able to move to the next energy level and superconductivity will collapse.

2.2 Gap in the energy spectrum

The first indications of the existence of an energy gap were obtained from the exponential law of decay of the electronic heat capacity of a superconductor:

c es ~ g T k e - bTk / T ~ c ns e - bTk / T . (16)

The energy gap in superconductors is directly observed experimentally, and not only is the existence of the gap in the spectrum confirmed, but its magnitude is also measured. The transition of electrons through a thin non-conducting layer ~10E thick, separating the normal and superconducting films, was studied. In the presence of a barrier, there is a finite probability of an electron passing through the barrier. In a normal metal all energy levels are filled, up to the maximum e F , in a superconducting metal up to e F -D. In this case, the passage of current is impossible.

The presence of an energy gap in a superconductor leads to the absence of corresponding states between which a transition would occur. In order for the transition to occur, the system must be placed in an external electric field. In the field, the entire picture of levels shifts. The effect becomes possible if the applied external voltage becomes equal to D/e. The tunnel current appears at a finite voltage U, when eU is equal to the energy gap. The absence of a tunneling current at an arbitrarily low applied voltage is proof of the existence of an energy gap.

Currently, a number of methods have been developed to detect such a gap and measure its width. One of them is based on studying the absorption of electromagnetic waves in the far infrared region by metals. The idea of the method is as follows. If a stream of electromagnetic waves is directed onto a superconductor and their frequency u is continuously changed, then as long as the energy of the quanta V of this radiation remains less than the gap width E w (if there is one, of course), the radiation energy should not be absorbed by the superconductor. At the frequency зк, for which ђш к = Е ь, intense absorption of radiation should begin, increasing to its values in a normal metal. By measuring shk, you can determine the width of the gap E sh.

Experiments have fully confirmed the presence of a gap in the energy spectrum of conduction electrons in all known superconductors. As an example, the table shows the gap width E w at T = 0 0 K for a number of metals and the critical temperature of their transition to the superconducting state. From the data in this table it is clear that the gap E is very narrow ~ 10 -3 -10 -2 eV; There is a direct connection between the gap width and the critical transition temperature Tc: the higher Tc, the wider the gap Ec. theory

The BCS leads to the following approximate expression relating T k with E sh (0):

E sh (0) = 3.5 kT k, (17)

which is quite well confirmed by experience.

In the theory of superconductivity, most results were obtained for the isotropic model. Real metals are actually anisotropic, which is evident in many experiments. Under fairly broad assumptions, we can obtain the formula:

where is the unit vector in the direction of impulse p; and is the Fermi radius vector of the surface and the velocities on it. The magnitude depends on the direction. According to experimental data, the change. At the same time, the temperature dependence is the same for all directions, i.e. .

Table 1.

Substance
E sh (0),10 -3 eV

E = 3.5 kT k

Anisotropy is already visible when comparing theoretical and experimental data for heat capacity. At low temperatures

where is the minimum gap, and according to the theoretical curve (for an isotropic model), where is some average gap. Therefore, as a rule, the theoretical curve at is lower than the experimental one.

There are various methods for more detailed determination of gap anisotropy. Thus, measuring the thermal conductivity of single-crystal single-core superconductors makes it possible to determine whether the minimum gap is located in the direction of the main axis or lies in the basal plane. The nature of the gap anisotropy can also be established from experiments with a tunnel contact if one of the superconductors is a single crystal. The most interesting results on anisotropy are obtained from experiments on sound absorption. If the frequency of sound is the binding energy of pairs, then at low temperatures absorption occurs only on excitations, i.e. proportionally. However, we must take into account that the mechanism of sound absorption is the inverse Cherenkov effect. This means that sound is absorbed only by those electrons whose velocity projection onto the direction of sound propagation coincides with the speed of sound, i.e. . But the speed of electrons in a metal is cm/sec, and the speed of sound is cm/sec; this means that, i.e. perpendicularly, in other words, sound is absorbed by electrons lying on the contour resulting from the intersection of the Fermi surface with a plane perpendicular. In view of this, low-temperature sound absorption is determined by the minimum value of the gap on this contour. By changing the direction of sound propagation, you can obtain fairly detailed information about the gap.

The anisotropy of the gap is also manifested in the fact that the change in thermodynamic quantities when defects are introduced into the superconductor is greater than for the isotropic model. For example, with a decrease compared to (for pure metal), i.e. proportional to the mean square anisotropy.

2.3 Gapless superconductivity

In the first years after the creation of the BCS theory, the presence of an energy gap in the electronic spectrum was considered a characteristic sign of superconductivity, but superconductivity without an energy gap is also known - gapless superconductivity.

As was first shown by A.A. Abrikosov and L.P. Gorkov, with the introduction of magnetic impurities, the critical temperature effectively decreases. Atoms of a magnetic impurity have spin, and therefore a spin magnetic moment. In this case, the spins of the pair appear to be in a parallel and antiparallel magnetic field of the impurity. With an increase in the concentration of atoms and magnetic impurities in a superconductor, an increasing number of pairs will be destroyed, and in accordance with this, the width of the energy gap will decrease. At a certain concentration n equal to 0.91n cr (n cr is the concentration value at which the superconducting state completely disappears), the energy gap becomes equal to zero.

It can be assumed that the appearance of gapless superconductivity is due to the fact that when interacting with impurity atoms, some pairs are temporarily broken. This temporary decay of the pair corresponds to the appearance of local energy levels within the energy gap itself. As the impurity concentration increases, the gap becomes increasingly filled with these local levels until it disappears completely. The existence of electrons formed when the pair breaks leads to the disappearance of the energy gap, and the remaining Cooper pairs ensure that the electronic resistance is zero.

We come to the conclusion that the existence of a gap in itself is not at all a necessary condition for the manifestation of a superconducting state. Moreover, gapless superconductivity, as it turns out, is not such a rare phenomenon. The main thing is the presence of a bound electronic state - a Cooper pair. It is this state that can exhibit superconducting properties even in the absence of an energy gap.

2.5 Electron pair formation

Forbidden bands in the energy spectrum of semiconductors arise due to the interaction of electrons with the lattice, which creates a field in the crystal with a periodically varying potential.

It is natural to assume that the energy gap in the conduction band of a metal in a superconducting state arises due to some additional interaction of electrons that appears during the transition of the metal to this state. The nature of this interaction is as follows.

A free conduction band electron, moving through the lattice and interacting with ions, slightly “pulls” them away from the equilibrium position (Figure 5), creating in the “wake” of its motion an excess positive charge, to which another electron can be attracted. Therefore, in a metal, in addition to the usual Coulomb repulsion between electrons, an indirect attractive force may arise due to the presence of a lattice of positive ions. If this force turns out to be greater than the repulsive force, then the combination of electrons into bound pairs, which are called Cooper pairs, becomes energetically favorable.

When Cooper pairs are formed, the energy of the system decreases by the amount of binding energy Eb of the electrons in the pair. This means that if in a normal metal the electrons of the conduction band at T = 0 K had a maximum energy E F , then upon transition to a state in which they are bound in pairs, the energy of two electrons (pairs) decreases by E St, and the energy of each of them - by E st /2, since this is exactly the energy that must be expended in order to destroy this pair and transfer the electrons to the normal state (Fig. 6a). Therefore, between the upper energy level of electrons in bonded pairs and the lower level of normal electrons there must be a gap of width E, which is precisely what is necessary for the appearance of superconductivity. It is easy to verify that this gap is mobile, that is, capable of shifting under the influence of an external field along with the electron distribution curve among states.

In Fig. Figure 7 shows a schematic model of a Cooper pair. It consists of two electrons moving around an induced positive charge, somewhat reminiscent of a helium atom. Each electron in a pair can have a large momentum and wave vector; the pair as a whole (the center of mass of the pair) can be at rest, having zero translational speed. This explains the at first glance incomprehensible property of electrons populating the upper levels of the filled part of the conduction band in the presence of a gap (Fig. 6a). Such electrons have enormous (and) translational speeds. Since the central positive charge of the pair is induced by the moving electrons themselves, under the influence of an external field, the Cooper pair can move freely throughout the crystal, and the energy gap E will shift along with the entire distribution, as shown in Fig. 6b. Thus, from this point of view, the conditions for the appearance of superconductivity are satisfied.

Fig.5 Fig. 7

However, not all conduction band electrons are capable of bonding into Cooper pairs. Since this process is accompanied by a change in the energy of the electrons, only those electrons that are capable of changing their energy can bond in pairs. These are only electrons located in a narrow strip located near the Fermi level (“Fermi electrons”). A rough estimate shows that the number of such electrons is ~ 10 -4 of the total number, and the width of the strip is, in order of magnitude, 10 -4.

In Fig. a Fermi sphere with radius is constructed in momentum space.

There are rings of width dl on it, located relative to the p y axis at angles q1, q2, q3. electrons whose vectors end up on the area of a given ring form a group with almost the same momentum. The number of electrons in each such group is proportional to the area of the corresponding ring. Since as μ increases, the area of the rings also increases the number of electrons in their corresponding groups. Generally speaking, electrons from any of these groups can bond into pairs. The maximum number of pairs is formed by those electrons that are larger. And most of all electrons, whose momenta are equal in magnitude and opposite in direction. The ends of the vectors of such electrons are located not on a narrow strip, but along the entire Fermi surface. There are so many of these electrons compared to any other electrons that practically only one group of Cooper pairs is formed - pairs consisting of electrons having momenta of equal magnitude and opposite direction. A remarkable feature of these pairs is their momentum ordering, which consists in the fact that the centers of mass of all pairs have the same momentum, equal to zero when the pairs are at rest, and different from zero, but the same for all pairs when the pairs move along the crystal. This leads to a fairly strict correlation between the movement of each individual electron and the movement of all other electrons bound in pairs.

The electrons “move like climbers tied together with a rope: if one of them fails due to the unevenness of the terrain (caused by the thermal movement of atoms), then its neighbors bring it back.” This property makes a collective of Cooper pairs less susceptible to scattering. Therefore, if the pairs are brought into orderly motion by one or another external influence, then the electric current created by them can exist in the conductor for an indefinitely long time, even after the cessation of the action of the factor that caused it. Since such a factor can only be the electric field E, this means that in a metal in which Fermi electrons are bound into Cooper pairs, the excited electric current i continues to exist unchanged even after the cessation of the field: i=const at E=0. This is evidence that the metal is indeed in a superconducting state, possessing ideal conductivity. Roughly, this state of electrons can be compared with the state of bodies moving without friction: such bodies, having received an initial impulse, can move for as long as desired, keeping it unchanged.

Above we compared the Cooper pair with the helium atom. However, this comparison should be taken very carefully. As already noted, the positive charge of the pair is unstable and strictly fixed, like that of a helium atom, but induced by the moving electrons themselves and moving with them. In addition, the binding energy of electrons in a pair is many orders of magnitude lower than their binding energy in a helium atom. According to the data in Table 1, for Cooper pairs E light = (10 -2 -10 -3) eV, while for helium atoms E light = 24.6 eV. Therefore, the size of a Cooper pair is many orders of magnitude larger than the size of a helium atom. The calculation shows that the effective diameter of the pair is L? (10 -7 -10 -6) m; it is also called the coherence length. The volume L 3 occupied by the pair contains the centers of mass of ~ 10 6 other such pairs. Therefore, these pairs cannot be considered as some kind of spatially separated “quasi-molecules”. On the other hand, the resulting colossal overlap of the wave functions of all pairs enhances the quantum effect of electron pairing to its macroscopic manifestation.

There is another analogy, and a very deep one, between Cooper pairs and helium atoms. It consists in the fact that a pair of electrons is a system with an integer spin, just like atoms. It is known that helium superfluidity can be considered as a manifestation of the specific effect of boson condensation at the lower energy level. From this point of view, superconductivity can be considered as a kind of superfluidity of Cooper pairs of electrons. This analogy goes even further. Another helium isotope, whose nuclei have half-integer spin, does not have superfluidity. But the most remarkable fact, discovered quite recently, is that as the temperature decreases, atoms can form pairs quite similar to Cooper’s, and the liquid becomes superfluid. Now we can say that superfluidity is like the superconductivity of pairs of its atoms.

Thus, the process of electron pairing is a typical collective effect. The attractive forces that arise between electrons cannot lead to the pairing of two isolated electrons. Essentially both the entire collective of Fermi electrons and the atoms of the lattice participate in the formation of a pair. Therefore, the binding energy (gap width E w) depends on the state of the collective of electrons and atoms as a whole. At absolute zero, when all Fermi electrons are bound in pairs, the energy gap E q reaches its maximum width E q (0). With increasing temperature, phonons appear that are capable of imparting energy to electrons during scattering, sufficient to break the pair. At low temperatures, the concentration of these phonons is low, as a result of which cases of electron pair breaking will be rare. The breaking of some pairs cannot lead to the disappearance of the gap for the electrons of the remaining pairs, but makes it somewhat narrower; The gap boundaries approach the Fermi level. With a further increase in temperature, the concentration of phonons increases very quickly, in addition, their average energy increases. This leads to a sharp increase in the rate of electron pair breaking and, accordingly, to a rapid decrease in the energy gap width for the remaining pairs. At a certain temperature Tk the gap disappears completely, its edges merge with the Fermi level and the metal goes into the normal state.

2.5 Effective interaction between electrons due to metal phonons

Fröhlich showed that the interaction of electrons with phonons can lead to effective interaction between electrons. Below we will outline the main provisions of his theory.

In an ideal lattice, the motion of an electron in the conduction band is determined by the Bloch function

which represents a plane wave modulated by a function u k (r) satisfying the periodicity condition u k (r) = u k (r+n), where n is the grating vector, k is the wave vector; h y is a function of the spin state. We will not need its explicit form and the form of the function u k (r) further.

The electron wave function of the entire metal containing N electrons in volume V is the antisymmetric product of the N function q k,y. The ground state corresponds to the filling of states lying in k - space inside the Fermi surface. We will assume that this surface lies far from the zone boundary and is isotropic, that is, it is a sphere of radius k 0 . upon excitation, electrons from states |k|< k 0 переходят в состояния k| >k 0 .

If е k is the energy of the electron state with quasi-momentum ђk, then in the representation of secondary quantization the Hamiltonian of the electron system (up to a constant term) has the form

where a + kу, a kу are the Fermi operators of creation and annihilation of quasiparticles.

To determine the operator of interaction with phonons of the metal lattice, we take into account that when a positive ion occupying the nth place in the lattice is displaced by an amount about n, the energy of interaction of the electron with the lattice will change by the amount. Therefore, in the representation of secondary quantization, the electron-phonon interaction operator can be written in the form

where is the operator expressed through the Fermi operators a kу and Bloch functions using the equality

The ion displacement operator is defined, therefore,

Where, are Bose operators; s is the speed of longitudinal sound waves corresponding to the wave vector q, since only longitudinal waves make a contribution and for them u(q) = sq.

Taking into account that the sum, if, and is equal to zero, if, we obtain the final expression for the electron-phonon interaction operators in the representation of occupation numbers

where (1825) is an abbreviated designation for the sums of products of Fermi operators; - a small value that determines the electron-phonon interaction. Integration is carried out over one elementary cell. Letters "es." the terms Hermitian conjugate to all previous ones are indicated.

The interaction operator (24) does not depend on the spin state of the electrons, so in what follows we can omit writing the spin index y. Operator (24) was obtained under the assumption that the ions in the lattice move as a single unit, that D(q) depends only on q and does not depend on k, and that the vibrations of ions in the lattice are divided into longitudinal and transverse for all values of q, so interaction occurs only with longitudinal phonons. Without these simplifications, calculations become very complicated. Such complication is justified only if it is necessary to obtain quantitative results.

INTRODUCTION

The phenomenon of superconductivity (1911) was discovered three years after liquid helium was obtained. At normal pressures, helium becomes liquid at a temperature of ~ 4.2 K. The Dutch physicist K. Kamerlingh Onnes discovered that at such low temperatures the electrical resistance of some metals abruptly vanishes.

The metal sample is connected to a voltage source and cooled with liquid helium. The voltage drop across the sample, measured by a voltmeter, became zero when the temperature dropped below a certain critical Tc. In an alternative embodiment, a ring of superconductor was placed in a magnetic field perpendicular to its plane. After turning off the magnetic field, an induction current was excited in the ring. In ordinary metals this current quickly decays. In a superconductor, the current remains and flows for an infinitely long time. Currently, subtle experiments show that the resistivity of a superconductor is at least no higher than . This value in
less than the resistivity of a good conductor - copper. Let us estimate the decay time of the superconducting current.

Rice. 1. Relationship between B and T c.

Later it was discovered that the superconducting state is destroyed not only when the temperature rises above a certain Tk, but also at the limiting values of the magnetic field and superconducting current (Vk and Ik). In Fig. 1 shows an approximate relationship between

SUPERCONDUCTOR AND IDEAL CONDUCTOR

Since a superconductor has a resistance very close to zero, it was believed for a long time that the properties of an ideal conductor (R = 0) and a superconductor are the same. But it turned out that this is only true for electrical resistance. In a magnetic field, differences between the corresponding samples are detected. Let's take an ideal conductor at a temperature less than Tc. When it is introduced into a magnetic field, the zero magnetic flux will remain zero, since eddy currents arise in the sample to compensate for the increase in the external magnetic flux (hence the magnetic induction B = 0). If you turn on the magnetic field at a temperature above the critical temperature, then cool the sample, then in this case the magnetic field will remain in the ideal conductor. The resulting eddy currents will not allow it to change.

In a superconductor, as Meissner and Ochsenfeld discovered in 1933, the magnetic field is always zero. If a sample of a superconductor transforms into a superconducting state, then the magnetic field inside it immediately becomes zero, regardless of whether the sample was in an external magnetic field before the transition or not.

The magnetic field is forced out of the superconductor. Hence the conclusion is drawn that a superconductor and an ideal conductor are fundamentally different in nature.

REVIEW OF SUPERCONDUCTIVITY THEORIES

The first attempt to explain superconductivity was the theory of the brothers G. London and F. London (1935). Equations were obtained that describe many of the properties of superconductors. It was assumed that electrons in a superconductor can be considered in the form of two groups: superconducting and normal electrons (two-fluid model).

At zero degrees, all electrons become superconducting. As the temperature increases, the density of superconducting electrons decreases and goes to zero at T=Tc. Superconducting electrons experience no resistance when moving. An electric field is not needed for such movement - superconducting electrons move as if by inertia. In the absence of an electric field, normal electrons are at rest.

A superconductor exhibits no resistance only when the current is constant. In the case of alternating current, the resistance is nonzero and the higher the frequency of the alternating current, the greater.

The magnetic field is not zero in a thin surface field, the thickness of which is given by

Ginzburg and Landau applied a phenomenological approach to the theory of superconductivity, taking into account the quantization of the phenomenon and described it as a second-order phase transition. A second-order phase transition is a transition without a change in the state of aggregation. Only the symmetry of the crystal lattice and the course of the temperature dependence of physical quantities change.

Later (1961) Deaver and Fairbank experimentally discovered the quantization of magnetic flux associated with a superconducting ring. Let's place the ring in a magnetic field at T > T c . Let's lower the temperature and transfer the ring to a superconducting state, then turn off the magnetic field. According to the Faraday-Lenz law, an induction current will arise, which will prevent the magnetic flux from changing. Since the ring resistance is zero, this current will not decay. Moreover, the value of such a “frozen magnetic flux” cannot be arbitrary. And is expressed by the formula

, where n is an integer.
In a normal conductor, the passage of current is accompanied by the release of heat (Joule-Lenz law). This heat arises from the collisions of electrons with the crystal lattice. The kinetic energy of electrons is converted into lattice vibration energy (thermal energy).

Then the essence of the phenomenon of superconductivity can be formulated as follows: at low temperatures, the crystal lattice for some reason cannot receive energy from moving electrons. Why? To understand the phenomenon of superconductivity, we must remember that electrons and atoms in crystals obey the laws of quantum mechanics, according to which energy can only be transferred in certain portions - quanta. Both the energies of free electrons in the crystal and the vibrations of the crystal lattice are quantized. The quantum nature of lattice vibrations manifests itself as temperatures approach absolute zero. The lattice can transfer to an electron only a very specific energy - the energy of a vibrational quantum. Then superconductivity could arise if the vibrational energy quantum were smaller than the distance between the electron energy levels. In this case, one quantum of vibration would not be enough to transfer the electron to another energy level. However, this is not so - electrons in metals are almost free and the distance between levels is negligible. Therefore, even at very low temperatures, individual electrons freely exchange energy with the lattice.

Theoretically, the problem of superconductivity in pure metals was solved by Bardeen, Cooper and Schrieffer by creating a theory called the BCS theory. They suggested that electrons, due to interactions with vibrations of the crystal lattice, form pairs called Cooper pairs. Superconducting current is the directed movement of pairs of electrons that occurs under the influence of an electric field. However, electrons interact with lattice vibrations separately. Therefore, in order to transfer energy to a pair, lattice vibrations must first destroy the pair and then transfer energy to one of the electrons.

Cooper pairs have internal symmetry, to understand which we need to remember some principles of quantum mechanics. Electrons obey the Pauli principle, i.e. There can be no more than one electron in one quantum state. Due to the Pauli principle, all electrons in a solid cannot have zero momenta. The conduction electron pulses successively fill a volume in momentum space bounded by a surface called the Fermi surface. In the theory of solids, it is customary to use instead of momentum p the wave vector k, which is related to momentum by the relation:

Р = nk
Electrons have one more, purely quantum degree of freedom - spin. For a visual interpretation, spin is represented as the rotation of an electron around its axis. Just as there are two directions of rotation for an arbitrarily chosen axis of rotation, there are two directions of spin up and down. Therefore, at each point in momentum space there can be two electrons with spins up and down. Obviously, due to the Pauli principle, electrons located deep inside the Fermi surface cannot change their momentum by a small amount, because all nearby levels are occupied. Only electrons located near the Fermi surface participate in conduction. When a field is applied, electrons near the Fermi surface change their momentum. The Pauli principle does not prevent this, because neighboring states are free. This is how ordinary current arises in conductors.

Now we need to understand how a superconducting current can arise. It is known from quantum mechanics that when two electrons interact, two energy levels arise: one with an energy greater than the sum of the energies of the two states, and the other with less energy. And a pair of electrons occupies the lowest energy level. Now, before transferring momentum to the electron, lattice vibrations must destroy the pair, and for this, the energy of the quantum of lattice vibrations must be greater than the binding energy of the pair. Thus, the BCS had to find the type of interaction between electrons and determine the structure of the pair. According to the BCS theory, two electrons with opposite momenta lying on the Fermi surface are bound into a pair. The total momentum of the pair is zero. When an electric field is applied, the momentum of the electrons in the pair changes slightly, and the center of mass of the pair begins to move in the direction opposite to the direction of the intensity vector. The electrons in a Cooper pair in a conventional superconductor pair have opposite spins. Such a pair is called singlet. The energy of the pair decreases due to interaction with phonons (lattice vibrations). The last assumption is confirmed by the isotope effect. Atoms were replaced by isotopes - atoms with the same number of protons, but with a different atomic mass, and the transition temperature changed. Since the energy of lattice vibrations depends on the mass of the atoms, from the presence of the isotopic effect a conclusion is drawn about the nature of the attractive potential between electrons. An important property of classical BCS superconductors is also the isotropy (spherical symmetry) of Cooper pairing. All electrons with a certain momentum, regardless of its direction, simultaneously form Cooper pairs as the temperature decreases.

Let us now formulate the basic properties of superconductors, which follow from the BCS theory:

Cooper pairs are singlets (the spins of the electrons in the pair are directed in opposite directions).
The superconducting state is spherically symmetric
Magnetic fields prevent superconductivity.
Superconductivity is due to electron-phonon interaction.
Superconductivity is observed in pure metals.

ABRikosov's whirlwinds

To explain the mechanism of penetration of a magnetic field into the surface of a type II superconductor, the concept of electron vortices, developed by A. A. Abrikosov and confirmed experimentally, turned out to be very fruitful. In the simplest case, the vortex is a thin cylindrical tube (with a radius of about 0.1 μm), through which the magnetic flux can penetrate into the superconductor (Fig. 2). The magnetic field is maintained in the vortex by electric currents that flow around the axis of the tube.

Figure 2. Scheme of the mixed state (Shubnikov phase). The magnetic field and superconducting circular currents are shown on two vortex filaments.

A vortex is essentially a hole in a superconductor and the magnetic flux passing through it must be quantized. According to Abrikosov's solution, the vortices form a regular lattice, the structure of which in the case of a mixed state was established in experiments on elastic neutron scattering.

PROBLEMS OF HIGH TEMPERATURE SUPERCONDUCTIVITY

In 1986, the work of Müller and Bednorz appeared, in which superconductivity was discovered in the oxides La 1.8 Ba 0.2 CuO 4 at unusually high temperatures T c = 100 K. This new type of superconductivity was called high-temperature HTSC. It is noteworthy that the work for which the Nobel Prize was subsequently given was not published in the most prestigious the physical journal Physical Review, published in the USA, and in the German journal Zeitschrift Fur Fusik. The fact is that the authors initially sent the article to Physical Review, but the reviewers rejected the article: because superconductivity in oxides, and even at such a high temperature, cannot exist! A similar story happened with these same compounds in the USSR. These compounds were synthesized by I. S. Shaplygin and V. B. Lazarev at the USSR Academy of Sciences in 1979. The authors discovered an unusual temperature dependence of conductivity in these compounds. They did not test for superconductivity at lower temperatures, because they could not assume that their samples were superconducting. They checked this only after Muller and Bednorets!

But even 2-3 years before the discovery of HTSC, superconductors were obtained not with such a record Tc, but with equally unusual properties - the so-called superconductors with heavy fermions TFSC. These are UPt 3, (T c =0.55 K) UBe 13 (T c =0.8 K) Sr 2 RuO 4 (T c =1.5K), UPd 2 Al 3 (T c =2K), PrOs 4 Sb 12 (T c =1.85 K). HTSC and TFSC are united in one word - unusual superconductors. According to the currently accepted definition, superconductors are those whose superconducting state is not spherically symmetrical, i.e. There is no Cooper pairing at some points and on the lines of the Fermi surface. Unusual superconductors differ experimentally from ordinary ones in the temperature dependence of physical quantities. In conventional superconductors, the temperature dependence of physical quantities such as thermal conductivity is exponential. In unusual superconductors, the temperature dependence of physical quantities is power-law.

Another important property of the superconducting state is its parity, i.e. how the wave function of a pair changes under the influence of spatial inversion I. In school geometry, centrally symmetrical figures are considered, which do not change when the sign of all coordinates is changed, and figures that do not have this property. In quantum mechanics, if the crystal structure is centrally symmetric, then two states are possible, characterized by the action of inversion I on the wave function Ψ(R). Even state:

Odd state:

According to the law of quantum mechanics, if the spins of electrons in a pair are directed oppositely (singlet pair), then the wave function is even, and if they are the same (triplet pair), then the wave function is odd. Experimental studies of new types of superconductors have discovered that in many of them the superconducting state has an odd wave function and the spins of the electrons in the pair are parallel. This allowed us to conclude about one more unusual property: superconductivity in some of them (UBe 13 UPt 3 Sr 2 RuO 4, UPd 2 Al 3 PrOs 4 Sb 12) has a triplet character, but in others, for example, in HTSC, it is singlet.

Electron-electron interactions always result in the fact that due to the interaction of two one-electron states, two possible multi-electron states arise, one with lower energy (ground) and the other with higher energy (excited) and both electrons occupy the ground state. The type of interaction determines which state will be the main one - singlet or triplet. Despite the fact that over the past 20 years many theories have been created, and the number of publications is in the thousands, the types of interactions leading to superconductivity in unusual superconductors are not yet reliably known. It is only known that in many TFSPs the interaction of electrons in a pair is associated with magnetism. Some atoms in crystals have their own magnetic moments due to the fact that the spins of atomic electrons are oriented in parallel. The moments of neighboring atoms can be oriented parallel - this structure is called ferromagnetic, or antiparallel - this structure is called antiferromagnetic. In many unusual superconductors (for example, UBe 13, UPt 3), an antiferromagnetic transition is observed when the temperature is lowered to approximately 10 T c. The coexistence of antiferromagnetic structure and superconductivity is reliably observed in UPd 2 Al 3, and spontaneous magnetic fields are detected in Sr 2 RuO 4 and PrOs 4 Sb 12. Thus, if in BCS superconductors the magnetic field destroys superconductivity, then in unusual superconductors internal magnetic fields somehow maintain superconductivity.

CONCLUSION

Let us now formulate 5 main features of unusual superconductors:

Cooper pairs can be either singlet or triplet.
The superconducting state is not spherically symmetric. On the Fermi surface there are lines and points where Cooper pairing is absent.
Superconductivity is somehow related to the magnetic structure of the crystal.
The specific interactions leading to superconductivity are unknown, it is only clear that the nature of these interactions may vary.
Superconductivity is observed in intermetallic compounds and ionic crystals.

We see that these five features of unusual superconductors are fundamentally different from the features of ordinary superconductors. The existing theory (BCS theory) correctly describes a particular case, but is not universal. Subsequent studies have refuted many of her general conclusions, but have not refuted her logic. This gives hope that the problem of high-temperature superconductivity will be solved and superconductors that operate at room temperature will be created.

Another promising direction of research into the mechanism of high-temperature superconductivity is the study of the mechanism of saltatory conduction of neurons with spiral myelin sheaths. Apparently, the formalism of the Abrikosov quantum vortex model can be applied to them.

LITERATURE

Tsypenyuk Yu. M. Physical foundations of superconductivity. - M.: 1996.
Kholmansky A. S. Modeling of brain physics // Mathematical morphology. Electronic mathematical and medical-biological journal. – T. 5. – Issue. 4. - 2006. - URL: www.smolensk.ru/user/sgma/MMORPH/N-12-html/holmansky-4/holmansky-4.htm

The Problems of high temperature overconduction

Lobach

ev V.V., Yargemskiy V.G., Kholmanskiy A.S.

Review of some problems of high temperature overconduction carry out.
*Moscow State University of Environmental Engineering (MGUEE).

**Moscow State Medical and Dental University (MGMSU)

Helium was first liquefied in 1908 by Heike Kamerlingh Onnes at the University of Leiden, and since then it has been possible to study physical phenomena at temperatures only a few degrees above absolute zero (the boiling point of helium at atmospheric pressure is 4.2 K).

One of the areas of research concerned the dependence of the resistance of metals on temperature. Kamerlingh Onnes has already carried out similar studies at temperatures decreasing down to the temperature of liquid air (about 80 K).

For several pure metals he found an approximately linear relationship, but he found that such a relationship could not continue indefinitely, since otherwise the resistance would become negative at absolute zero. Sir James Dewar continued Kamerlingh Onnes's research and reached the temperature of liquid hydrogen (20 K), and it turned out that the resistance actually began to decrease more slowly.

This is exactly what should have been expected, not only for the reason already mentioned, but also based on the ideas about metals and their properties accepted at that time.

It was believed that electrical conductivity occurs through the transfer of electrons, and resistance arises as a result of collisions of electrons with metal atoms.

The linear nature of the decrease in resistance was quite consistent with the expected change in the movement of electrons with decreasing temperature. It was expected, however, that at sufficiently low temperatures electrons would “condense” on the atoms, then the resistance at some temperature should be minimal, and then the metal should become an insulator.

The behavior of metals observed in reality differed sharply from that assumed. Kamerlingh Onnes discovered that as the temperature decreases, the resistance of most metals tends to a constant value, while for some metals it completely disappears at a certain characteristic temperature, which, as it turned out, depends on the strength of the magnetic field. These experiments are among the works for which Kamerlingh Onnes was awarded the 1913 Nobel Prize in Physics.

For more than two decades, it was the disappearance of resistance that was considered the main, distinguishing feature of superconductivity. However, some features of this phenomenon have confused scientists.

So, if a magnetic field is applied to an ordinary conductor (not a ferromagnet), part of the magnetic flux passes through the thickness of the conductor. If you apply it to an ideal conductor, surface currents are induced in the latter, which create a magnetic field inside the conductor that completely compensates for the applied external field, and thereby maintain a zero magnetic flux value inside the conductor.

This meant that the state of a conductor in a magnetic field depended on how this state was achieved - a highly unpleasant situation.

Later, in 1933, W. Meissner, R. Ochsenfeld and F. Heidenreich showed that a metal, becoming a superconductor, actually expels a magnetic flux if the temperature drops below a critical value when the sample is in a magnetic field.

The next stage of the study was to study the newly discovered state at high current values. The need for such a study was dictated by the following circumstance: if the resistance were not actually zero, then a larger current would have to lead to a larger, and therefore easier to record, value of the potential difference.

However, the results obtained only further confused the situation, since a “special phenomenon” was observed: at any temperature below 4.18 K for a mercury filament enclosed in a glass capillary, there was a certain threshold current density value, above which the nature of the phenomenon changed sharply. At current densities below the threshold electric current passes without any noticeable potential differences applied to the ends of the filament. This indicated that the thread had no resistance.

As soon as the current density exceeded the threshold value, a potential difference appeared, which also grew faster than the current itself.” Then a series of experiments was carried out to find an explanation for the new effect. First of all, it was noticed that the threshold current density increased with decreasing temperature - approximately proportional to the deviation from the transition temperature to the superconducting state (as long as the difference between the temperatures was not too large). Naturally, the assumption was that due to heating caused by some effect, the temperature of the mercury rose above the transition point. The task was set to find this heat source.

Using different configurations of the mercury filament, it was possible to establish that heat was not supplied from outside. The influence of impurities in mercury was considered, although they should have been removed during the distillation process; experiments have shown that the heating effect is not associated with impurities specially added in the required quantities.

It was further suggested that perhaps contact of a mercury filament with an ordinary conductor, in some form found in it or formed within it, could cancel the superconducting properties of mercury. A steel capillary was taken for testing, but this did not lead to any definite results, and only later, as a result of experiments of the same type on tin, this assumption was excluded. In general, experiments with mercury did not answer the question posed.

However, as Kamerlingh Onnes established, mercury was not a very suitable object for systematic research. “The combined effect of many circumstances led to difficulties when working with mercury in capillaries.

A day of experimenting with liquid helium required a huge amount of preparation, and when it came to the actual experiments described here, there were only a few hours left for them. In order to make accurate measurements with liquid helium under these conditions, it is necessary to outline a program in advance and carry it out quickly and methodically on the day of the experiment. Changes in the experimental setup, the need for which was caused by the observed phenomena, usually had to be made the next day.

Often, due to some delay caused by the labor-intensive process of manufacturing resistances, the helium installation was used for some other purpose. When we could start the experiment again, it happened that the prepared resistances turned out to be useless, since when the mercury was frozen, the thread broke, and all our efforts became in vain. Under these conditions, it took a very long time to detect and eliminate sources of unexpected and misleading interference.

In addition, it was desirable to cool the sample not through the capillary wall, but by direct contact with liquid helium. Therefore, when Kamerlingh Onnes discovered that tin and lead had properties similar to those of mercury, he continued experimenting with these two metals. It was then that the problem posed was solved.

In fact, hope for its solution arose already during experiments in which the superconductivity of lead was discovered. It could easily be made into wire, and quite a large amount of wire was made, with a cross-section of 70 mm2. For a single conductor of this size, the threshold current value at 4.25 K was 8 A. Next, a coil 1 cm long containing 1000 turns was wound with this wire on a core with a diameter of 1 cm. The winding had silk insulation, which is wetted with liquid helium. As it turned out, the threshold current value was only 0.8 A.

In 1913, interest in obtaining strong magnetic fields was already quite great, and there was no doubt that the main problem was related to power dissipation in the winding. For example, Perrin proposed using liquid air for cooling; it was expected that due to a decrease in the resistance of the winding with a decrease in temperature, the amount of heat generated in it would decrease, which would give a certain gain.

Calculations have shown, however, that gains cannot be achieved in this way, primarily due to the fact that it is very difficult to achieve the required heat transfer between the supposedly compact coil and the cooler. Kamerliig-Onies correctly assessed the possibilities of using superconductors for this purpose, noting that no heat should be generated in them at all. While speaking about this, he did, however, admit "the possibility that a magnetic field could lead to resistance in the superconductor." And he began to study this issue.

“There were reasons to believe that this effect would be weak. Direct proof that superconductors experience only a slight resistance under the influence of a magnetic field was obtained when it turned out that the coil described above remains superconducting even if a current of 0.8 A passes through it. The field of the coil itself in this case reached several hundred gauss , and most of the turns were in a field of this order of magnitude, but no resistance was observed.” Therefore, Kamerlingh Onnes created a setup for conducting these experiments that would make it possible to study phenomena observed only in fields of the order of kilogauss.

The results were again unexpected. The superconducting lead coil used in previous experiments was placed in a cryostat so that the plane of the turns was parallel to the magnetic field.

“First of all, we were convinced that the coil would be superconducting at the boiling point of helium; it remained superconducting even when a current of 0.4 A was passed through it, although the turns were in a noticeable magnetic field created by the current flowing through them.

Then a magnetic field was applied. At a field strength of 10 kG there was significant resistance; at 5 kG it was somewhat less. These experiments showed quite convincingly that a magnetic field at high intensity causes the appearance of resistance in superconductors, but at low intensity it does not. In the course of further research, the dependence of the resistance on the field was obtained.

Kamerlingh Onnes was not yet ready to connect the critical current with the critical value of the magnetic field. He had no doubt that the phenomenon discovered here was connected with the sudden appearance at a certain temperature of ordinary resistance in superconductors - this connection was discovered by other researchers. Nevertheless, it could be considered that the foundation was laid.

Over time, however, the paradox described at the beginning of this chapter has become very apparent. A slight change in wording made it even stronger. If a substance, being in a magnetic field, was to transform into an ideally conducting state as the temperature decreases, then the magnetic flux penetrating the sample at the moment of transition should remain “frozen” into it and persist when the field is subsequently turned off (if the temperature is maintained unchanged) .

By preparing different samples in this way, it would be possible to create a multitude (in principle, an infinite number) of different states existing under the same external conditions, which could perhaps even be in thermal contact with each other, i.e., in a state of equilibrium.

Until 1933, this possibility was not refuted experimentally, and some experiments even seemed to confirm it. There were even theoretical considerations in its favor. And at that moment, Meissner, studying the transition to the superconducting state, was struck by the appearance of a kind of hysteresis: the return of the tin single crystal to the normal state occurred at a temperature slightly higher than the temperature of the transition to the superconducting state.

This effect was observed even when the resistance at each point was measured in two directions of current by a method specially designed to exclude thermoelectric phenomena; if the direction of the current did not change, the effect was enhanced. The hysteresis suggested that the phenomenon was associated with a change in the permeability of the sample.

Meisner wrote about it this way: “If the distribution of the measured current and the magnetic field created by it did not change, there would be no basis for the occurrence of hysteresis phenomena.” Therefore, he and his collaborators assume that its permeability drops to zero. If this were the case at all, then no field line could end at the inner surface of the superconductor cavity, whereas experiments clearly show that this is exactly the situation.

Many years passed before a satisfactory theory of superconductivity could be created; in fact, this issue was not finally resolved even in 1972. However, Meissner's discovery at least made it possible to give a satisfactory macroscopic interpretation of the observed phenomena.

J. Trigg "Physics of the 20th Century: Key Experiments"

A brief overview of the theories of superconductivity and the problems of high-temperature superconductivity are analyzed. School encyclopedia

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INTRODUCTION

SUPERCONDUCTOR AND IDEAL CONDUCTOR

REVIEW OF SUPERCONDUCTIVITY THEORIES

ABRikosov's whirlwinds

PROBLEMS OF HIGH TEMPERATURE SUPERCONDUCTIVITY

CONCLUSION

LITERATURE

The Problems of high temperature overconduction