Unconventional superconductivity in two-dimensional electron systems with long-range correlations

We explore salient features of high-Tc superconductivity in two-dimensional electron liquid, that are triggered by critical fluctuations enhanced in the vicinity of an impending second order phase transition. A simple theoretical explanation for the transition from d-wave to another type of superconducting pairing that has recently observed in the electron-doped cuprates is offered. The dx2−y2 pairing potential Δ, which has maximal magnitude at the hot spots on the Fermi surface, becomes suppressed under increase of electron doping, because the hot spots approach the Brillouin zone diagonals where the respective gap value vanishes, and pairing with dx2−y2 symmetry is then replaced by either singlet s-wave or triplet p-wave pairing. We argue in favor of p-wave pairing and propose experiments to verify this assertion. The phenomenon of flattening of electron spectra in high-Tc superconductors is discussed. We suggest that this phenomenon can be explained on the basis of the Fermi liquid approach, involving unconventional solutions emerging beyond the point where stability conditions for the traditional Landau state are violated. The problem of pairing in anisotropic electron systems possessing patches of fermion condensate in the vicinity of the van Hove points is analyzed. Attention is directed to opportunities for the occurrence of non-BCS pairing correlations between the states belonging to the fermion condensate. It is shown that the physical emergence of such pairing correlations would drastically alter the behavior of the single-particle Green function, the canonical pole of Fermi-liquid theory being replaced by a branch point.