Ginzburg - Landau Expansion in BCS - BEC Crossover Region of Disordered Attractive Hubbard Model

We have studied disorder effects on the coefficients of Ginzburg - Landau (GL) expansion for attractive Hubbard model within the generalized DMFT+Sigma approximation for the wide region of the values of attractive potential U - from the weak-coupling limit, where superconductivity is described by BCS model, towards the strong coupling, where superconducting transition is related to Bose - Einstein condensation (BEC) of compact Cooper pairs. For the case of semi-elliptic initial density of states disorder influence on the coefficients A and B before the square and the fourth power of the order parameter is universal for at all values of electronic correlations and is related only to the widening of the initial conduction band (density of states) by disorder. Similar universal behavior is valid for superconducting critical temperature T_c (the generalized Anderson theorem) and specific heat discontinuity at the transition. This universality is absent for the coefficient C before the gradient term, which in accordance with the standard theory of "dirty" superconductors is strongly suppressed by disorder in the weak-coupling region, but can slightly grow in BCS - BEC crossover region, becoming almost independent of disorder in the strong coupling region. This leads to rather weak disorder dependence of the penetration depth and coherence length, as well as the slope of the upper critical magnetic field at T_c, in BCS - BEC crossover and strong coupling regions.Comment: 22 pages, 12 figures, as published in I.M. Lifshitz centenary issue of Low Temperature Physic

Reconstruction of the Fermi surface in the pseudogap state of cuprates

Reconstruction of the Fermi surface of high-temperature superconducting cuprates in the pseudogap state is analyzed within nearly exactly solvable model of the pseudogap state, induced by short-range order fluctuations of antiferromagnetic (AFM, spin density wave (SDW), or similar charge density wave (CDW)) order parameter, competing with superconductivity. We explicitly demonstrate the evolution from "Fermi arcs" (on the "large" Fermi surface) observed in ARPES experiments at relatively high temperatures (when both the amplitude and phase of density waves fluctuate randomly) towards formation of typical "small" electron and hole "pockets", which are apparently observed in de Haas - van Alfen and Hall resistance oscillation experiments at low temperatures (when only the phase of density waves fluctuate, and correlation length of the short-range order is large enough). A qualitative criterion for quantum oscillations in high magnetic fields to be observable in the pseudogap state is formulated in terms of cyclotron frequency, correlation length of fluctuations and Fermi velocity.Comment: 4 pages, 3 figure