Phenomenological Ginzburg-Landau-like theory for superconductivity in the cuprates

Abstract

We propose a phenomenological Ginzburg-Landau-like theory of cuprate superconductivity. The free energy is expressed as a functional F of the spin-singlet pair amplitude psi_ij=psi_m=Delta_m exp(i phi_m); i and j are nearest-neighbor sites of the Cu lattice in which the superconductivity is believed to primarily reside and m labels the site at the center of the bond between i and j. The system is modeled as a weakly coupled stack of such planes. We hypothesize a simple form, F[Delta,phi]=sum_m (A Delta_m^2+ B Delta_m^4/2)+C sum_ Delta_m Delta_n cos(phi_m-phi_n), for the functional. The coefficients A, B and C are determined from comparison with experiments. We work out a number of consequences of the proposed functional for specific choices of A, B and C as functions of hole density x and temperature T. There can be a rapid crossover of from small to large values as A changes sign on lowering T and the crossover temperatures is identified with the observed pseudogap temperature. The superconducting phase-coherence transition occurs at a different temperature T_c, and describes superconductivity with d-wave symmetry for C>0. We calculate T_c(x) which has the observed parabolic shape, being strongly influenced by the coupling between Delta_m and phi_m present in F. The superfluid density, the local gap magnitude, the specific heat (with and without a magnetic field) and vortex properties are obtained using F. We compare our results successfully with experiments. We also obtain the electron spectral density as influenced by the coupling between the electrons and the pair correlation function calculated from F. Features such as temperature dependent Fermi arcs, antinodal pseudogap filling temperature, pseudogapped density of states in different momentum regions of the Fermi surface and `bending' of the energy gap versus momentum on the Fermi surface emerge from the theory.