Analytical Results for Cold Asymmetrical Fermion Superfluids at the Mean-Field Level

TL;DR

This paper provides analytical mean-field results for asymmetric fermion superfluids with attractive interactions at zero temperature, exploring phase behavior and competition between different ground states.

Contribution

It offers explicit analytical expressions involving elliptic integrals for asymmetric fermion superfluids, detailing phase transitions and ground state competition at the mean-field level.

Findings

Asymmetry influences ground state phases and transitions.

Two candidate phases compete depending on asymmetry and pairing gap.

Degeneracy occurs between phases at infinite pairing gap.

Abstract

We present the analytical results at the mean-field level for the asymmetrical fermion system with attractive contact interaction at the zero temperature. The results can be expressed in terms of linear combinations of the elliptic integrals of the first and second kinds. In the limit of small gap parameter, we discuss how the asymmetry in fermion species affects the phases of the ground state. In the limit of large gap parameter, we show that two candidate phases are competing for the system's ground state. The Sarma phase containing a pure Fermi fluid and a mixed condensate is favored at large degree of asymmetry. The separated phase consisting of a pure Fermi fluid and a boson condensate supports the system at smaller degree of asymmetry. The two phases are degenerate in the limit of infinite pairing gap.