The pseudogap state in superconductors: Extended Hartree approach to time-dependent Ginzburg-Landau Theory

TL;DR

This paper extends the Hartree approximation within the time-dependent Ginzburg-Landau framework to develop a mean field theory for pseudogapped superconductors, capturing strong coupling effects and their impact on transport properties.

Contribution

It introduces a generalized mean field theory for pseudogapped superconductors that incorporates strong coupling and relates fermionic and bosonic behaviors within a unified framework.

Findings

Recasting Ginzburg-Landau equations in T-matrix form enables analysis of strong coupling.

Identification of two contributions to transport below T_c: fermionic and bosonic.

Bosonic transport described effectively by time-dependent Ginzburg-Landau theory.

Abstract

It is well known that conventional pairing fluctuation theory at the Hartree level leads to a normal state pseudogap in the fermionic spectrum. Our goal is to extend this Hartree approximated scheme to arrive at a generalized mean field theory of pseudogapped superconductors for all temperatures $T$. While an equivalent approach to the pseudogap has been derived elsewhere using a more formal Green's function decoupling scheme, in this paper we re-interpret this mean field theory and BCS theory as well, and demonstrate how they naturally relate to ideal Bose gas condensation. Here we recast the Hartree approximated Ginzburg-Landau self consistent equations in a T-matrix form. This recasting makes it possible to consider arbitrarily strong attractive coupling, where bosonic degrees of freedom appear at $ T^*$ considerably above $T_c$. The implications for transport both above and below $T_c$ are discussed. Below $T_c$ we find two types of contributions. Those associated with fermionic excitations have the usual BCS functional form. That they depend on the magnitude of the excitation gap, nevertheless, leads to rather atypical transport properties in the strong coupling limit, where this gap (as distinct from the order parameter) is virtually $T$-independent. In addition, there are bosonic terms arising from non-condensed pairs whose transport properties are shown here to be reasonably well described by an effective time-dependent Ginzburg-Landau theory.