Superconducting fluctuations in the Luther-Emery liquid

TL;DR

This paper calculates the superconducting Green's functions in a Luther-Emery liquid using bosonization, revealing how phase fluctuations affect the spectral gap and its size dependence.

Contribution

It provides an asymptotic expression for the superconducting gap in a Luther-Emery liquid, incorporating phase fluctuations and their impact on spectral properties.

Findings

Superconducting gap exhibits a size-dependent power-law decay.

Spectral gap shows a singularity at the gap energy.

Comparison with 2-leg t-J ladder highlights similarities and differences.

Abstract

The single-particle superconducting Green's functions of a Luther-Emery liquid is computed by bosonization techniques. Using a formulation introduced by Poilblanc and Scalapino [Phys. Rev. B v. 66, art. 052513 (2002)], an asymptotic expression of the superconducting gap is deduced in the long wavelength and small frequency limit. Due to superconducting phase fluctuations, the gap exhibits as a function of size L a (1/L)^{1/2K_\rho} power-law decay as well as an interesting singularity at the spectral gap energy. Similarities and differences with the 2-leg t-J ladder are outlined.