Non-interacting Cooper pairs inside a pseudogap

TL;DR

This paper introduces an analytical model for the normal state of underdoped cuprate superconductors, showing how pseudogaps and fluctuating Cooper pairs influence spectral properties and the transition temperature.

Contribution

It provides a self-consistent approach linking pseudogap features, pairing fluctuations, and the pair condensation temperature in nearly two-dimensional superconductors.

Findings

Fermion spectral weight shows two BCS-like peaks broadened by fluctuations.

Density of states is suppressed near the Fermi energy, indicating a pseudogap.

Long-lived low-energy Cooper pairs propagate as a sound-like mode.

Abstract

I present a simple analytical model describing the normal state of a superconductor with a pseudogap in the density of states, such as in underdoped cuprates. In nearly two-dimensional systems, where the superconducting transition temperature is reduced from the mean-field BCS value, Cooper pairs may be present as slow fluctuations of the BCS pairing field. Using the self-consistent T-matrix (fluctuation exchange) approach I find that the fermion spectral weight exhibits two BCS-like peaks, broadened by fluctuations of the pairing field amplitude. The density of states becomes suppressed near the Fermi energy, which allows for long-lived low-energy Cooper pairs that propagate as a sound-like mode with a mass. A self-consistency requirement, linking the width of the pseudogap to the intensity of the pairing field, determines the pair condensation temperature. In nearly two-dimensional systems, it is proportional to the degeneracy temperature of the fermions, with a small prefactor that vanishes in two dimensions.