Superconducting properties of a nonideal bipolaron gas

Abstract

The properties of a Bose gas of translation-invariant (TI) bipolarons analogous to Cooper pairs are considered. As in the BCS theory, the description of a TI-bipolaron gas is based on the electron-phonon interaction and FroehlichHamiltonian. As distinct from the BCS theory, when the correlation length greatly exceeds the mean distance between the pairs, here we deal with the opposite case when the correlation length is much less than the distance between the pairs. We calculate the critical temperature of the transition of a TI-bipolaron Bose-gas into the superconducting state, its energy, heat capacity and heat of the transition. The results obtained are used to explain the experiments on high-temperature superconductors. Possible ways of raising the critical temperature of high-temperature superconductors are discussed.

Translation-invariant bipolaron theory of superconductivity and spectroscopic experiments

“…The theory developed in [1,2] fits in well with the thermodynamic properties of HTSC materials and their magnetic characteristics [5]. However, these facts alone do not enable us to conclude that the TI bipolaron theory of SC does not contradict other experimental facts.…”

“…In large part this is due to the fact that so fat a unified theory of HTSC has not been created. On the understanding that a SC mechanism is caused by Cooper pairing, in the case of strong Froehlich EPI this leads to the TI bipolaron theory of HTSC [1,2]. As distinct from bipolarons with broken symmetry, TI bipolarons are delocalized in space and do not have a polarization potential well (polarization charge is equal to zero).…”

“…In papers [1,2] we constructed a translation invariant (TI) bipolaron theory of superconductivity (SC) on the basis of a Hamiltonian of Pekar-Fröhlich electron-phonon interaction (EPI) when EPI, as distinct from the case of the Bardeen-Cooper-Schrieffer theory [3], cannot be considered to be weak. The role of Cooper pairs in this theory belongs to TI bipolarons whose correlation length (≈ 1nm) is much less than that of Cooper pairs (≈ 10 3 nm).…”

“…The role of Cooper pairs in this theory belongs to TI bipolarons whose correlation length (≈ 1nm) is much less than that of Cooper pairs (≈ 10 3 nm). According to [1,2], in high-temperature superconducting (HTSC) materials, TI bipolarons are formed near the Fermi surface and represent a charged Bose gas capable of experiencing Bose-Einstein condensation (BEC) at high critical temperature which determines the temperature of SC transition.…”

“…In the case of weak EPI (BCS limit), the frequency of an optical phonon is ω 0 >> |E B |, in the case of intermediate coupling it is ω 0 ∼ = |E B |, and in the case of strong coupling it is ω 0 << |E B |, where |E B | is the energy of a TI bipolaron. According to [2], the number of TI bipolarons N B is: N B ≈ N|E B |/2E F , where N is the total number of electrons, E F is the Fermi energy, i.e. N B << N. This means, in particular, that when calculating the London penetration depth in the TI bipolaron theory in order to find the concentration of superconducting current carriers at low temperatures, one should use N B , rather than the total number of current carriers N as one does in the BCS.…”