Abstract
A translation-invariant (TI) bipolaron theory of superconductivity based, like Bardeen–Cooper–Schrieffer theory, on Fröhlich Hamiltonian is presented. Here the role of Cooper pairs belongs to TI bipolarons which are pairs of spatially delocalized electrons whose correlation length of a coupled state is small. The presence of Fermi surface leads to the stabilization of such states in its vicinity and a possibility of their Bose–Einstein condensation (BEC). The theory provides a natural explanation of the existence of a pseudogap phase preceding the superconductivity and enables one to estimate the temperature of a transition T * from a normal state to a pseudogap one. It is shown that the temperature of BEC of TI bipolarons determines the temperature of a superconducting transition T c which depends not on the bipolaron effective mass but on the ordinary mass of a band electron. This removes restrictions on the upper limit of T c for a strong electron-phonon interaction. A natural explanation is provided for the angular dependence of the superconducting gap which is determined by the angular dependence of the phonon spectrum. It is demonstrated that a lot of experiments on thermodynamic and transport characteristics, Josephson tunneling and angle-resolved photoemission spectroscopy (ARPES) of high-temperature superconductors does not contradict the concept of a TI bipolaron mechanism of superconductivity in these materials. Possible ways of enhancing T c and producing new room-temperature superconductors are discussed on the basis of the theory suggested.
Highlights
The theory of superconductivity for ordinary metals is one of the finest and long-established branches of condensed matter physics which involves macroscopic and microscopic theories and derivation of macroscopic equations from a microscopic description [1]
The results of [17] enabled one to develop the idea of a crossover, i.e., passing on from the Bardeen–Cooper–Schrieffer theory (BCS) theory which corresponds to the limit of weak electron-phonon interaction (EPI) to the Bose–Einstein condensation (BEC) theory which corresponds to the limit of strong EPI [18,19,20,21,22,23,24]
A replacement of a real interaction by a local one in the BCS enabled one to derive the phenomenological Ginzburg-Landau model which is a local model [37]. The power of this approach can hardly be overestimated since it enabled one to get a lot of statements consistent with the experiment. Another more important reason why the crossover theory failed is that vacuum in the polaron theory with spontaneously broken symmetry differs from the vacuum in the translation invariant (TI) polaron (TI bipolaron) theory in the case of strong interaction which makes it impossible for the Eliashberg theory to pass on to the strong coupling TI bipolaron theory (Section 2)
Summary
The theory of superconductivity for ordinary metals is one of the finest and long-established branches of condensed matter physics which involves macroscopic and microscopic theories and derivation of macroscopic equations from a microscopic description [1]. The results of [17] enabled one to develop the idea of a crossover, i.e., passing on from the BCS theory which corresponds to the limit of weak electron-phonon interaction (EPI) to the BEC theory which corresponds to the limit of strong EPI [18,19,20,21,22,23,24] (see review [25]). The power of this approach can hardly be overestimated since it enabled one to get a lot of statements consistent with the experiment Another more important reason why the crossover theory failed is that vacuum in the polaron (bipolaron) theory with spontaneously broken symmetry differs from the vacuum in the translation invariant (TI) polaron (TI bipolaron) theory in the case of strong interaction which makes it impossible for the Eliashberg theory to pass on to the strong coupling TI bipolaron theory (Section 2). According to the TI bipolaron theory of SC, a natural explanation is provided for such phenomena as the occurrence of kinks in the spectral measurements of a gap, angular dependence of a gap, the availability of a pseudogap, etc
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