Superconductivity with hard-core repulsion: BCS-Bose crossover and s-/d-wave competition

TL;DR

This paper investigates the interplay of superconductivity and repulsive interactions in a 2D lattice, revealing a crossover from BCS to Bose-Einstein condensation and the emergence of unconventional gap structures.

Contribution

It introduces a mean-field approach that accounts for on-site repulsion, showing the resulting gap function can develop nodes, and explores the BCS-Bose crossover in this context.

Findings

s-wave Bose condensed state is the ground state in dilute, strong coupling limit

Superconducting gap function can have radial nodes due to on-site repulsion

Presence of next-neighbor hopping t' can induce nodes on the Fermi surface

Abstract

We consider fermions on a 2D lattice interacting repulsively on the same site and attractively on the nearest neighbor sites. The model is relevant, for instance, to study the competition between antiferromagnetism and superconductivity in a Kondo lattice. We first solve the two-body problem to show that in the dilute and strong coupling limit the s-wave Bose condensed state is always the ground state. We then consider the many-body problem and treat it at mean-field level by solving exactly the usual gap equation. This guarantees that the superconducting wave-function correctly vanishes when the two fermions (with antiparallel spin) sit on the same site. This fact has important consequences on the superconducting state that are somewhat unusual. In particular this implies a radial node-line for the gap function. When a next neighbor hopping t' is present we find that the s-wave state may develop nodes on the Fermi surface.