Stability conditions and Fermi surface topologies in a superconductor

TL;DR

This paper investigates the stability of various superconducting states with mismatched chemical potentials, identifying conditions under which they are stable or unstable, with implications for ultracold fermionic atom systems.

Contribution

It analyzes stability criteria for gapless superconductors with different Fermi surface topologies, emphasizing number susceptibility as a key constraint.

Findings

Two-zero Fermi surface states are mechanically unstable.

Number susceptibility positivity constrains stable phases.

Results applicable to ultracold fermionic atom experiments.

Abstract

Candidate homogeneous, isotropic superfluid or superconducting states of paired fermion species with different chemical potentials, can lead to quasiparticle excitation energies that vanish at either zero, one, or two spheres in momentum space. With no zeroes, we have a conventional BCS superconductor. The other two cases, ``gapless'' superconductors, appear in mean field theory for sufficiently large mismatches and/or sufficiently large coupling strengths. Here we examine several stability criteria for those candidate phases. Positivity of number susceptibility appears to provide the most powerful constraint, and renders all the two-zero states that we have examined mechanically unstable. Our results should apply directly to ultracold fermionic atom systems.