Stability of the Breached Pair State for a Two-species Fermionic System in the Presence of Feshbach Resonance

TL;DR

This paper explores the stability of breached pair states in a two-species fermionic system with Feshbach resonance, revealing conditions under which single Fermi-surface states can be stable and estimating experimental parameters for $^6$Li.

Contribution

It demonstrates that breached pair states with two Fermi surfaces are unstable, but single Fermi-surface states can be stable under specific conditions related to Feshbach parameters.

Findings

Breached pair states with two Fermi surfaces are always unstable.

Single Fermi-surface breached pair states can be stable if chemical potentials have opposite signs.

Stability conditions are characterized by narrow magnetic field regions on the BEC side.

Abstract

We investigate the phenomenon of fermionic pairing with mismatched Fermi surfaces in a two-species system in the presence of Feshbach resonance, where the resonantly-paired fermions combine to form bosonic molecules. We observe that the Feshbach parameters control the critical temperature of the gapped BCS superfluid state, and also determine the range over which a gapless breached pair state may exist. Demanding the positivity of the superfluid density, it is shown that although a breached pair state with two Fermi surfaces is always unstable, its single Fermi-surface counterpart can be stable if the chemical potentials of the two pairing species have opposite signs. This condition is satisfied only over a narrow region in the BEC side, characterized by an upper and a lower limit for the magnetic field. We estimate these limits for a mixture of two hyperfine states of $^6$Li using recent experimental data.