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Abstract:
Development of superconductors which can operate at room temperature has been a major focus of interest of physicists all over the world. At times news come out about the discovery of new high-temperature (HTSC) materials which brings hope that such superconductors will be developed. At present, however, a unified theory of such materials is lacking. Victor Lakhno, a physicist from Keldysh Institute of Applied Mathematics, suggested to take the translation-invariant bipolaon theory as a basis. In the paper published in Advances in Condensed Matter Physics possible ways of solving the room-temperature superconductivity problem are presented.

Theory gives free rein to superconductivity at room temperature

Moscow, Russia | Posted on May 28th, 2018

Generally accepted BCS theory for which its originators Bardeen, Cooper and Schrieffer were awarded the Noble Prize in 1972, discarded the phenomenon of superconductivity at temperature close to absolute zero (near -270°C). However in 1986 by way of experiments Alex Müller and Georg Bednorz found a molecular entity belonging to the class of high-temperature superconducting cuprates La2-xBaxCuO4 (?=-243°C), for what they also received the Nobel Prize. These materials received the name HTCS materials. By now scientists have already created materials superconducting at temperatures up to -70°Celsius. Today the main problem is to develop of a microscopic theory capable of explaining experimental facts which cannot be accounted for by the standard BCS theory. This has given rise to a multitude of new explanations of the superconductivity mechanism. One of them is a bipolaron scenario.

Victor Lakhno, head of the Laboratory of Quantum-Mechanical Systems of the Institute of Mathematical Problems of Biology, RAS -- the Branch of Keldysh Institute of Applied Mathematics RAS has calculated a critical temperature of the transition, energy, heat capacity and heat of transition of an ideal three-dimensional Bose-condensate of translation-invariant bipolarons (TI-bipolarons). The results obtained offer an explanation of the experiments with high-temperature superconductors.

Bose-Einstein condensate -- is a state of matter which was predicted by Albert Einstein and Satyendra Nath Bose in 1925. The condensate in itself was produced 70 years later, in 1995, by Eric Cornell and Carl Wieman in a gas of rubidium cooled to nearly absolure zero (1,7×10-7 K). For their achievements Cornell and Wieman received the Nobel Prize in 2001. In a Bose-condensate all the particles move consistently. They form one quantum-mechanical wave and behave like one huge particle. All of them are located in one and the same place and at the same time each of them is "spread" over the whole region of space. Victor Lakhno mathematically proved that a quantum Bose-gas consisting of translation-invariant bipolarons in a one-dimensional conductor can give birth to a Bose-condensate.

A polaron is a quasiparticle consisting of electrons and excitations which electrons induce while moving through a crystal lattice. Such excitations are called phonons. The notion of a polaron was introduced by a soviet physicist Solomon Pekar in 1946. Later the theory of polarons was developed by Alexander Tulub who found a new solution of the polaron problem for the case of a strong interaction between an electron and a lattice. A bipolaron is a pair of polarons bounded by a phonon interaction. Victor Lakhno has managed to show that a polaron can be translation-invariant, i.e. be a plane wave running in a crystal lattice. He theoretically proved that translation-invariant bipolarons can produce a stable Bose-condensate in stripes even at room temperature. This means that superconductivity at these temperatures is possible.

In his calculations he proceeded from the same factors as the classical BCS theory did. However He excluded the electron variables from the Froehlich Hamiltonian of electron-phonon interaction instead of the phonon ones. Since in the case of a linear dispersion law (as in the BCS) phonons represent quantized acoustic waves, it can be said that in the TI-bipolaron theory, SC is caused by charged acoustic waves which form a SC condensate. In the case of HTSC materials, according to his theory, we deal not with acoustic phonons, but with optic ones since these materials are ionic crystals. As a result, the theory describes a charged Bose gas of optical phonons coupled with electron pairs which are translation-invariant (TI) bipolarons. Like Cooper pairs TI-bipolarons are plane waves possesing a small correlation length equal to several constants of the crystal lattice.

The qualitative difference of this theory from the other ones is that it implies that even at zero temperature only a small portion of all the electrons are in the TI-bipolaron (paired) state. This corresponds to the results obtained in Bo�ovi? et al experiments in 2016 and opens up new opportunities for creation of room-temperature superconductors. Since this theory suggests that in order to enhance the critical temperature of the transition, one should enhance the concentration of TI-bipolarons.

Viktor Lakhno tells: "To produce a superconducting cable operable at room temperature one should use strongly underdoped HTSC material (whose SC transition temperature is very low, i.e. a few K). This material, however, already contains bipolarons, though in very small quantity. It only remains to enhance their concentration without resort to doping. This can be arranged by making the cable coaxial so that the internal small-diameter cable isolated from the external one could induce a strong electric field attracting bipolarons".

Earlier the problem has never been formulated in this way, since it was believed that at low temperatures all the electrons are paired anyway and one can only enhance the concentration of electrons, not their pairs.

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