The modern theory of conventional superconductivity is based upon the concept of quantum states with broken gauge symmetry providing non-zero values for the so-called "anomalous averages" [Formula: see text], [Formula: see text]. Being applied to the simplest Gorikov-like semiphenomenological electronic scenario for a metal superconductor, this idea (in the mean field approximation) leads towards a complete description of all properties of ordinary superconductors as a manifestation of macroscopic quantum phase coherence. Currently there exists already strong experimental evidence that the newly discovered high Tc superconductors exhibit the same quantum coherence effects including the highly characteristic quantity for these phenomena, namely the doubled electronic charge. On these grounds one can expect that the high Tc superconductors should also be described by "anomalous averages" of the same kind. The only question is whether Gorikov's scenario is still sufficient or we need a new scenario instead in order to grasp the whole situation. In the case of Gorikov's scenario one needs to explain how the strong electron-electron coupling (no matter of what origin) can be consistent with the system stability condition. Yet there is another argument in favour of a new scenario. The large variety of the new SC properties cannot be explained by a model with too limited number of physical parameters. In our dealing with the problem of a possible new scenario we have suggested that in order to understand the high T c superconductors one should not perhaps go so far as to doubt the one-particle approximation and to introduce the Hubbard-like models, RVB and so on. Taking into account the crystalline structure of perfect high T c superconductors we have assumed within the one-particle description the two overlapping bands approach which was proposed by Suhl, Mattias and Walker (USA) and Moskalenko (USSR) as early as in 1959. To obtain qualitatively new results we have suggested a sharp asymmetry between the two bands (one being practically a local energy level close to the Fermi level) and also a special structure of direct electron-electron interaction with dominating interband scattering of singlet electron pairs described by an amplitude g. As the final analysis has shown, an inevitable but comparatively small splitting of the two bands does not invalidate the results of the model. As to the peculiar structure of interaction we believe it might be explained through a strong electron-optical phonon coupling due to the Jahn-Teller-like instability manifested in tetragonal-orthorhombic transitions of HT c samples. The model just outlined can indeed yield high T c . In the mean field approximation (with two superconductivity order parameters) the order of magnitude of T c is given by T c ~ (|g|N(o)/2)2 EF where N(o) is the density of states in the wide band at the Fermi level and EF is a wide band width. There is an exponentially sharp decline of T c while overdoping or underdoping the system and there is also a broad plateau when the narrow band is filled partially (the heavy fermion situation). The other results of calculations including thermodynamics and also kinetic properties for the normal state do not contradict experiments except for the linear temperature dependence of the specific heat observed sometimes. But one must take into account that in reality all high T c superconductors are in fact disordered solutions, and it is necessary to consider the dirty alloy limit with Anderson's theorem being violated because of the narrow band existence. At the same time, as analysis shows, the mean field approximation is not good enough for the model (the small parameter is only ( log 2/|g|N(o))-1) and therefore one has to apply Green's functions technique in order to correct the results. There is also a possibility that the magnetic properties connected with localized spins (if there are any) must be taken into account as well.
Phase Diagram of the Attractive Kane-Mele-Hubbard Model at Half Filling
