The Story of the Superconductor: The explanation of the Inexhaustible Current and the B.C.S. Theory

The Explanation of the Inexhaustible Current and the B.C.S. Theory

The Explanation of the Inexhaustible Current and the B.C.S. Theory

In the previous episode, we discussed the history of the discovery of superconductivity. At the time, scientists did not understand the cause of the source. The concept of electron religion needed to explain superconductivity came in later times, after the discovery of quantum theory. This is what we are discussing in this episode.

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Attraction between electrons

Superconductivity was successfully explained by three scientists - John Burdin, Leon Cooper, and John Robert Schriefer. This famous theory with the initials of their names is called B. C. S. In the name of the theory. The theory was fully published in 1956. Earlier, many prominent scientists have struggled to unravel the complexities of superconductivity. Their contribution is also significant in the history of this discovery. But we will not go into that detailed history.
According to the B.C.S theory, the force of attraction between two electrons - the source of superconductivity!
According to the B. C. S. theory, superconductivity is born when electrons attract each other. Many may be surprised to hear! We have always known that the repulsive force acts according to Coulomb's law between two electrons.

Where did the attraction come from? In fact, the contact of electrons and ions inside a solid material creates a seemingly attractive force between the electrons. In this article, we will try to give a very simplified description of that attraction.

Ions are many times more massive than electrons and move much slower than electrons. When an electron rapidly passes by an ion, the ion leans towards the electron due to its opposite charge. This causes a slight distortion in the row of icons, which results in the effect of a large positive charge or positive charge in one place. 

The second electron, which was coming the same way, was attracted to the accumulation of that positive charge. Then the matter became such that the first electron attracted the second electron by distorting it in the ionosphere. That binds two electrons together by attraction. These pairs are called Cooper pairs.

The victory of attraction overpowers repulsion

The idea that an attractive force can be created inside the electrons, mediated by ions, is B. C. S. The theory has been around for some years now. This idea was born by Herbert Froelich. Then the question arose - is this attraction so strong that the overall attraction will be effective even if it overcomes the normal repulsion of the electrons?

The answer came from the later works of David Bohm, David Pines, and John Burden. By calculating how the other electrons around an electron will affect this state, the effect of repulsion between the electrons can be ignored. 

Then in 1956, Leon Cooper proved that if an attractive force acts between electrons, no matter how small, the normal state of the electrons at absolute zero temperature would be the sum of the electrons attached in pairs.

This work by Leon Cooper B. C. S. One of the most important steps in discovering the theory. Earlier, scientists had realized that gravity between electrons could create a new state that was completely different from that of ordinary metals. 

But it was not known what the minimum level of attraction needed to be to get to this new stage. Cooper showed that even if it is infinitely small. On the whole, if the ball is attractive, a new phase will be seen at absolute zero temperature.

One year later, in 1958, John Bardin, Leon Cooper, and John Robert Schrieffer published the famous B.C.S. Theory. In many detailed calculations of quantum theory and statistical physics, they proved that when metal-free electrons are paired with each other in pairs, the superconductor phase is formed by the sum of the Cooper pairs at low temperatures.
This new phase of matter is the result of the rhythmic sum of numerous Cooper pairs - superconductivity.
Cooper pairs are very disciplined at this stage. Different pairs keep pace with each other. The theory is that in this case, the resistance will be zero. It is known that when the temperature rises, the rhythmic drop occurs at different stages of the formation of the Cooper pair. 

So if you keep raising the temperature of the material, once it is no longer a superconductor, it goes back to the normal metallic state again.

Alone fermion, Boson in pairs

Electrons have an intrinsic property called spin. The spin is the inherent angular momentum of a particle. Before the advent of quantum theory, scientists had no idea about the religion of the spin of particles.

 Although it is necessary to practice proper mathematical methods to understand the phenomena of the quantum world correctly, I am not going in that direction at the moment. It may be remembered that spin can be imagined as a directional sum - it can be described by a value and a direction. 

The spin value of some particles is an integer (e.g. 0, 1, 2, etc.), and in the case of others, the sum of the half with an integer (e.g. 1/2, 3/2, 5/2, etc.). The first type of particle is called a boson, and the second is called a fermion. Incidentally, the two scientists named after these two are Satyendranath Bose and Enrico Fermi.

In the aggregate of particles, the nature of each particle is described by the number of certain properties. Usually, these qualities are strength, momentum, spin, etc. These are called quantum numbers.

If the particles are fermions, all the quantum numbers of any two particles in their sum can't be equal. This rule is called Paulie Exclusion Principal. There are no such restrictions for bosons.

In the absence of this restriction, all boson particles are available at minimal energy at zero temperature. The electron is a fermion because its spin is 1/2, According to the  B.C.S theory that a Cooper pair is made up of a combination of two electrons, their spins must be opposite to each other. 

The spin of the two opposite poles is added according to the rules of quantum theory, so the spin of the Cooper pair stands at zero. The Cooper pair's religion is therefore much like that of the boson.

The integrated phase of electron pairing

This is a huge difference between a free metal electron and a Cooper pair made up of a combination of two electrons. The Cooper pairs of superconductors form a coherent state due to the boson-national religion, where they are closely bound to each other. What exactly is this integrated phase? 

Let's remember the scene of the army parade, which we see on the television screen on Republic Day. Everyone on the team moves with equal rhythm, speed. This is the solidarity of the Cooper pairs of the superconductor phase.

The B.C.S. theory shows how this integrated phase can explain the Mysner-Oxenfeld effect. If you remember, the Mysner-Oxenfeld effect was as follows: The magnetic field inside the superconductor disappears. 

When the superconductor is placed close to a magnet, it creates an inverse field, so that the total magnetic field inside it is zero.

After the discovery in the Meissner-Oxenfeld effect laboratory, in 1935, Fritz London and Heinz London showed that some equations could be determined using Maxwell's electromagnetic theory and zero resistance data in superconductors. 

From their solution, it is possible to explain the existence of the Mysner-Oxenfeld effect. If a magnetic field is present, an electric current is generated on the surface of the superconductor. 

That is why a new field appears around it which is the complete opposite of the outer field, so much so that the total field inside becomes zero. The theories of Fritz and Heinz London were built in the style of classical physics. At the microscopic level, they did not start calculating the nature of electrons.

The B.C.S. theory shows that the above equations can be established from the description of the combined phase of the Cooper pairs. The whole picture is clear.
A number of scientists have been awarded the Nobel Prize for their research on superconductivity.
By examining what was going on in the superconductor, what scientists saw in the laboratory where the conception of the B. C. S. was present. Their full description was found in the theory. Bardin, Cooper, and Schriefer were awarded the Nobel Prize in 1972 for this remarkable feat. After that, there is no reason to think that the veil of the superconductor's story has fallen. It was a big surprise for the future. 

In the next part, we would be mainly discussing The search for superconductivity at normal temperatures.

Author: Shamashis Sengupta, University of Paris — XI alumni.

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