The optimal inhomogeneity for superconductivity

TL;DR

This paper investigates how inhomogeneous transverse couplings influence superconductivity in quasi-one-dimensional systems, revealing an optimal inhomogeneity level that maximizes the pairing gap and discussing phase stability under disorder.

Contribution

It identifies the optimal degree of inhomogeneity for enhancing superconductivity and analyzes phase stability in multi-leg ladders with disorder.

Findings

Inhomogeneity generally increases the superconducting gap.

Beyond optimal inhomogeneity, phase coherence is suppressed.

Delocalized, spin-gapped phases are stable against weak disorder.

Abstract

We study the effect of nonuniform transverse couplings on a quasi-one dimensional superconductor. We show that inhomogeneous couplings quite generally increase the superconducting (pairing) gap relative to the uniform system, but that beyond an ``optimal'' degree of inhomogeneity, they lead to a suppression of the tendency to phase coherence. The optimal conditions for superconductivity are derived. We also show that a {\it delocalized}, spin-gapped phase is stable against weak disorder in a four-leg-ladder with moderate repulsive interactions.