Pairing imbalance in BCS-BEC crossover of inhomogeneous three-component Fermi-gas in two dimensions

TL;DR

This paper analytically explores the phase diagram of a three-component ultracold Fermi-gas in two dimensions, revealing how pairing imbalance affects the BCS-BEC crossover and phase separation.

Contribution

It provides an analytical study of the phase diagram for a three-component Fermi-gas with unequal chemical potentials in 2D, highlighting unique features of the Sarma phase and phase ratios.

Findings

Same particle density and condensed fraction as previous two-component studies.

Identification of Sarma phase as coexistence of normal and superfluid gases.

Minimum BCS phase ratio of 1/3 in the three-component system.

Abstract

We in this paper investigate the phase diagram associated with the BCS-BEC crossover of a three-component ultracold superfluid-Fermi-gas of different chemical-potentials and equal masses in two dimensions. The gap order parameter and number densities are found analytically by using the functional path-integral method. The balance of paring will be broken in the free space due to the unequal chemical-potentials. We obtain the same particle number-density and condensed fraction in the BCS superfluid phase as that in a recent paper (Phys. Rev. A 83, 033630), while the Sarma phase of coexistence of normal and superfluid Fermi gases is the characteristics of inhomogeneous system. The minimum ratio of BCS superfluid phase becomes 1/3 in the BCS limit corresponding to the zero-ratio in the two-component system in which the critical point of phase separation is {\epsilon}B/{\epsilon}F = 2 but becomes 3 in the three-component case.