Superconductivity. Quantum theor

There are many models of superconductivity, including the quantum mechanical theory of superconductivity. We will also add one hypothesis on this issue based on quantum mechanics.

A superconductor has two of the most important properties:

1. Zero electrical resistance.

2. The ability to push out magnetic flux (Meissner effect).

Quotes, as elsewhere, are in italics. Without specifying the source of the links, the quotes are from Wikipedia.

Here's how the academic science explains superconductivity:

“ The quantum mechanical theory of superconductivity (BCS theory) considers this phenomenon as superfluidity of a Bose-Einstein condensate of Cooper pairs of electrons in a metal with the absence of friction inherent in superfluidity. Conduction electrons move freely in the superconductor - without "friction" about the inhomogeneity of the crystal lattice ”.

Wonderful superfluidity of steam condensate. The speed of the current is equal to the speed of light, that is, 300,000 km / sec. Accordingly, the Cooper pair, without clinging to “ inhomogeneities of the crystal lattice ”, must move at the speed of light. While under normal conditions the speed of a simple electron in a conductor is about 0.5 m / s. A striking leap in speed.

Cooper pairs are formed by the attraction of electrons, and the attraction of electrons is facilitated by the crystal lattice.

The figure shows part of the lattice. The nodes contain metal ions. An electron 1 moves between the rows of ions. When an electron passes between two ions, its electric field attracts these ions to itself, or rather gives them an impulse to move towards itself. The ions begin to approach each other, creating an excess positive potential along the path of the electron. This excess potential drags another electron 2 with it, forming a Cooper pair. But this turns out to be a primitive understanding of the pairing process.

The site Elements contains the work of VL Ginzburg and EA Andryushin "Superconductivity". Chapter 3 “The Nature of Superconductivity” says:

“ The first comparison that comes to mind is that an“ electronic ”molecule has emerged. But it is not so. The atoms in the molecules are side by side, and in order to pass some "foreign" atom "through" the molecule, you need to spend a lot of energy, and the molecule will be destroyed. In a Cooper pair, electrons are located at a large distance, which can be thousands of times greater than the average distance between electrons, i.e. between the two electrons that make up a pair, a huge number of other electrons, belonging to other pairs, "run freely". ”.

This means that our electron 2 may be, or rather must be, away from the electron 1 like this so that the electrons 4 and 5 or 6 and 3 , could also form pairs without destroying the vibrational pattern between the electrons 1 and 2 . The distances between electrons are different for each material and they are called the correlation length. Since the electron generates vibrational motion of the lattice, this vibration was called a phonon. The correlation length appears to be essentially the phonon length.

The attraction of electrons is carried out by phonons - quanta of energy of sound frequency. In the same place, Ginzburg writes:

“ Recall that phonons are waves of the crystal lattice of a metal. However, it is equally possible to represent them as particles, which is accepted in quantum mechanics ”.

Now an utter leapfrog appears in the minds of the people. Wave-corpuscle dualism also manifests itself in the generation of phonons, and not only in Jung's experiment. In truth, this is one of the main laws of quantum mechanics, as Academician S. Gershtein says in his lectures. It is a pity that this is only accepted, but it might not have been accepted. Wikipedia read:

“ In the quantum theory of metals, the attraction between electrons (phonon exchange) is associated with the occurrence of elementary excitations of the crystal lattice. An electron moving in a crystal and interacting with another electron through the lattice transfers it to an excited state. At the transition of the lattice to the ground state, a quantum of sound-frequency energy is emitted — a phonon, which is absorbed by another electron. The attraction between electrons can be represented as an exchange of electrons by phonons, and the attraction is most effective if the momenta of the interacting electrons are oppositely directed ".

How one electron, interacting with another electron through the lattice, translates it into an excited state, it is impossible to understand. Then the lattice, returning to its original state, emits “ a quantum of sound-frequency energy - a phonon, which is absorbed by another electron ”. So the nucleus absorbed one phonon and then emitted it? It looks like an electron hit some string, the string sounded, the sound rolled to another electron, which absorbed it and generated a response sound itself. Or is there no need for sound? Then it should be said simply - a phonon is an electromagnetic wave with a frequency from 16 hertz to 20 kilohertz. This is roughly what we hear. And this would be perfectly fair, because a sound generator is not only a sound generator, but also a quantum generator, such as a light bulb, magnetron, or something else. The oscillating element moves the particles of the medium, in which there are electrons, and the accelerating electrons emit quanta.

Note that here, as in all physics, there is a lot of confusion between the concepts of phonon and quantum. Quantum is the smallest particle of anything, and each material has its own phonon. (see articles: "Quantum, what does it consist of" , "Quantum of energy, how it works and how it moves" and "Photon" ).

The situation looks strange when an electron whose mass is approximately 2,000 times less than the mass of a proton and approximately 2,000 * 100 times less than the mass of an ion, a conductor with an atomic weight of about 50, in which there are 50 protons and the same number of neutrons , can somehow move the ion without changing its direction and without losing a large amount of its kinetic energy. Of course, we can say that the electron will replenish energy due to the external field, which allows it to vibrate the lattice sites. But then how do these vibrations of ions differ from thermal vibrations? Only because they are more ordered, but external energy is still wasted. And this is no longer a superconductor.

Other provisions of this model also look strange.

In general, the Cooper pair model looks pretty unsatisfactory. Yes, it should be so, because it was built only in order to obtain a boson model of a particle from fermions. A priori, all physicists knew, and many still think so, that there is no "friction" in a Bose fluid, that is, a conductor does not resist Bose particles, while in a Fermi fluid there is such "friction". But two bound electrons have an integer spin, like bosons, and therefore do not interact with anything and can propagate without loss.

Why does a respected academic science give such a shaky and contradictory explanation of the phenomenon of superconductivity? Most likely, the fact is that science does not provide clear and clear concepts of the propagation of ordinary conductivity. There is no clear understanding of conduction current and bias current . For this reason, it is necessary to introduce the concept of a phonon instead of the displacement current.

The propagation of current on the shortest conductor, whether superconducting, whether with a Manganin resistance, or from one transformer winding to another, or from a transmitter antenna to an antenna on Voyager, has the same physical principle. An electron that receives energy in the form of acceleration (conduction current) from an energy source immediately transforms it into a photon (displacement current), which is directed to another electron. An electron that has received a photon can either retransmit this photon, according to Huygens, further, or absorb it and convert it into its kinetic energy, or change its energy state (store a photon as potential or, in other words, thermal energy). In a conductor, electrons are close to each other, but not close enough to push each other. This phenomenon is more pronounced in the generator. There may be no electrons between the windings of a transformer, not to mention a vacuum, in which there are no electrons.

If all the electrons and photons that come to the conductor transfer the energy received from the source through this conductor without loss, that is, not a single photon will be absorbed, then this will be the phenomenon of superconductivity. In such a conductor, not a single electron should come into the regime of kinetic motion. And the electron can come to the regime of kinetic motion only if the photon is resonant with the electron. The resonance properties of a free unbound electron depend only and only on its speed relative to vacuum. For a bound electron, the resonance properties strongly depend on the magnitude of these bonds, which are different for different substances.

It so happened in nature that most substances in normal conditions emit and absorb the same photons, that is, for each photon there is always a resonant receiver. But sometimes it is possible to create a generator that is not resonant for these successors or receivers that are not resonant for a given radiation. A striking artifact of this phenomenon is transceiver devices of various types. By turning the knob of the receiver, we can get a resonant structure for one or another radiation, in fact, for certain photons.

It is these resonant abilities in the elements of the conductor that we change by lowering the temperature. Depending on the magnitude of the voltage applied to the conductor, a corresponding spectrum of photons is generated. If the conditions are normal, then, depending on the properties of the conductor, some of the photons pass through it, and some are absorbed and stored in the form of heat (respectively, the heat capacity of the body). The process of heat absorption and release is continuous. Therefore, the resonance properties of the conductor are continuously closed and opened.

With a decrease in body temperature, its resonance properties relative to the emitted photons affecting this body may change. If the conductor is homogeneous, then all of its electrons, both free and bound, are in the same conditions, each in its own group. At a certain temperature, free electrons pass into such an energy state that they are not able to absorb photons of the displacement current, but can only transfer them to a friend without changing their speed regime. Approximately the same situation is observed with bound electrons, they occupy such levels that these photons at this voltage cannot move them to other levels. But as soon as the potential on the conductor is increased, photons with a different energy appear immediately, for which resonance properties are not closed at this temperature and superconductivity will be destroyed.

Why, when the temperature of the conductor decreases, its electrons lose their resonant properties and behave like repeaters? It is well known that an accelerated electron emits a photon. In an atom, such an electron will move to another level. Since the speed of the electron has increased, it goes to a level closer to the nucleus. Note that this is the physical essence of changing the size of bodies. The absorbed photon has covered part of the resonance properties of this electron. Now this electron, all photons with energy equal to the given absorbed photon and photons with energy less than the energy of this photon, can only retransmit them and cannot absorb them.

The lower the temperature, the less and less resonant properties of electrons. And there comes a critical temperature at which there are no resonant photons for electrons, all photons are only retransmitted, and the energy is not lost anywhere. But as soon as we increase the voltage, more powerful photons appear and superconductivity is again violated. And this will continue until the resonance region of the electrons goes beyond the spectrum of the radiation that we supply to the superconductor.

An apparent contradiction arises here. When we lower the temperature of a conductor, then according to the molecular view, the intensity of the movement of atoms decreases, and we all talked about increasing the speed of electrons. In reality, there is no contradiction: atomic and molecular speeds fall to a minimum, possibly to zero, and the speeds of electrons in an atom increase to a maximum, possibly to the speed of light. That is, it is possible that the electron completely passes into an equilibrium phase state between a mass (particle) and a photon (electromagnetic state) (see. atom device ).

It is clear that when the conductor does not absorb energy, then its heat capacity drops. This very moment is reflected in Figure 2.

And it is clear why superfluidity is obtained with superconductivity. Atoms in this state have minimum sizes and minimum spatial electric fields. They easily move relative to each other or relative to other elements. Penetrate any gap.

The nature of the change in heat capacity ( c _v , blue graph) and resistivity ( & rho; , green) during a phase transition to a superconducting state .

What happens when a superconductor is placed in a magnetic field? As Wikipedia narrates:

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

On the website "Eye of the Planet" in the article "Experimental confirmation of genus one and a half superconductivity is postponed" The Meissner effect is described as follows:

“ The phenomenon of superconductivity is characterized by zero electrical resistance of a substance and its ideal diamagnetism, which manifests itself in the pushing out and non-penetration of the magnetic field into the material. To be very precise, the magnetic field still penetrates the superconductor. But the depth of this penetration is very shallow and amounts to a maximum of about 100 nm. In such a thin layer, persistent currents are excited, which help the superconductor to screen the external magnetic field and prevent it from going deeper into the material. This is the reason for ideal diamagnetism, or the Meissner-Oxenfeld effect. The state of ideal diamagnetism of a superconductor is also called the Meissner state, and the screening currents are called Meissner currents. If we fix the temperature and begin to increase the “strength” of the magnetic field, then at a certain value of its induction B _c (critical field), superconductivity abruptly ceases to exist, since Meissner currents are no longer capable protect the superconductor from the intrusion of the external field. As a result, the substance passes from the superconducting state to the normal state (Fig. 1). Superconductors that behave in this way are called Type I superconductors ”. Figure 3

Let's try to understand how the screening of the magnetic field occurs. When the magnetic field changes near a conductor in any conduction state, a current arises in the conductor. This is an ordinary transformer. The changing field sets in motion the electrons of the conductor. Moving electrons create a magnetic field, which is precisely directed against the field that induced this current. If it were not so, then they would get a perpetual motion machine. The induced currents in a superconductor were called Meissner currents.

In the superconducting mode, as we have seen, electrons do not absorb anything, but they regularly move in an oscillatory mode, and therefore, even in a constant magnetic field, an induced field appears, directed against the external magnetic field. And since there are no losses in this mode of conversions, the compensation of the field of fields occurs completely. It looks like a skin effect.

It turns out that there are also superconductors of the second kind, in which the conductivity changes from the Meissner state to the normal state, not abruptly, but through a certain mixed state. In a mixed state in a conductor there are superconducting zones and zones with normal conductivity. Filaments of ordinary conductivity appear due to the penetration of a magnetic field into a superconductor, and they are formed by quantum vortices or Abrikosov vortices. Vortices are formed when the magnetic field is exceeded B _c1 (lower critical field) (third graph).

When an electron enters a superconducting mode, this does not mean that it cannot absorb photons below a certain energy, let's say 200 units of energy. Some electrons move to such levels that they cannot absorb photons of energy less than 210 or 223 units. It all depends on the pre-state in which the electron was before entering the superconducting mode. It is these states of electrons that organize the mixed state.

And one more thing - the existence of a type 1.5 superconductor was theoretically predicted by Yegor Babaev and Martin Speight. In this case, there is an intermediate state between the Meissner state and the mixed state. In this case, vortex "molecules" so-called by these scientists appear, which are then grouped into a vortex lattice.

True, Moshalkov failed to convincingly confirm this theoretical position, which is what the article under consideration is actually devoted to. It turned out that he observed these vortex "molecules" deep in the Meissner state. In Moshalkov's experiments, the interval is “deep” in the Meissner state, “… the Meissner state, according to various experimental estimates, fluctuates approximately from 0.003 to 0.01 T for the same temperature of 4.2 K”, and Moshalkov's experiments were carried out in “… the range of magnetic inductions: from 0.0001 T to 0.0005 T at a temperature of 4.2 K ".

This phenomenon can be clarified from the standpoint of photons (a photon is indeed a vortex structure in the sense of propagation), or rather their generation and absorption. Namely, everyone knows that a changing magnetic field induces a current in a conductor. The current is understood as the movement of electrons. A moving, or rather accelerating, electron emits (generates) quanta (photons). For an electron to return to its previous state, it must absorb exactly the same photon that it emitted.

That is, the magnetic field has opened up resonant opportunities for the electron, which is similar to an increase in temperature. It turns out that by lowering the temperature we are trying to calm down the chaotic movement of electrons, and the magnetic field provokes this movement, albeit more ordered. And the possibilities of exciting the motion of electrons in a magnetic field are quite a lot: both the magnitude of the magnetic field and the rate of its change. It is possible not only to change the speed of the electron, but also to reorient the spin of the electron, which sharply changes its resonance properties. For this reason, it is quite possible not only type one and a half superconductivity, but some other conductivities other than type 1 and type 2 superconductivity.