Stability Conditions in Gapless Superconductors

TL;DR

This paper analyzes the stability of gapless superconducting states with different Fermi surface configurations, revealing that single-Fermi-surface states are stable in certain regimes, while two-Fermi-surface states are universally unstable, with implications for ultracold atom systems.

Contribution

It provides a detailed stability analysis of gapless superconductors with varying Fermi surface structures, identifying conditions for their stability and instability.

Findings

Single Fermi surface gapless states are stable in the BEC region.

Two Fermi surface gapless states are unstable across all parameters.

Results are applicable to ultracold fermionic atom experiments.

Abstract

Gapless superconductivity can arise when pairing occurs between fermion species with different Fermi surface sizes, provided there is a sufficiently large mismatch between Fermi surfaces and/or at sufficiently large coupling constant. In gapless states, secondary Fermi surfaces appear where quasiparticle excitation energy vanishes. This work focuses on homogeneous and isotropic superfluids in the s-wave channel, with either zero (conventional superconductor), one, or two spherical Fermi surfaces. The stability conditions for these candidate phases are analyzed. It is found that gapless states with one Fermi surface are stable in the BEC region, while gapless states with two Fermi surfaces are unstable in all parameter space. The results can be applied to ultracold fermionic atom systems.