Phase Diagram of Cold Polarized Fermi Gas in Two Dimensions

TL;DR

This paper analytically maps the phase diagram of a two-dimensional polarized Fermi gas across the BCS-BEC crossover, revealing the nature of phase transitions, critical fields, and density profiles in harmonic traps.

Contribution

It provides a systematic analytical investigation of the superfluid-normal phase transition and density structures in 2D polarized Fermi gases, including critical parameters and shell structures.

Findings

First-order transition from superfluid to normal phase.

Analytical expressions for critical Zeeman fields and population imbalance.

Shell structure with superfluid core and polarized normal shell.

Abstract

The superfluid phase diagrams of a two-dimensional cold polarized Fermi gas in the BCS-BEC crossover are systematically and analytically investigated. In the BCS-Leggett mean field theory, the transition from unpolarized superfluid phase to normal phase is always of first order. For a homogeneous system, the two critical Zeeman fields and the critical population imbalance are analytically determined in the whole coupling parameter region, and the superfluid-normal mixed phase is shown to be the ground state between the two critical fields. The density profile in the presence of a harmonic trap calculated in the local density approximation exhibits a shell structure, a superfluid core at the center and a normal shell outside. For weak interaction, the normal shell contains a partially polarized cloud with constant density difference surrounded by a fully polarized state. For strong interaction, the normal shell is totally in fully polarized state with a density profile depending only on the global population imbalance. The di-fermion bound states can survive in the whole highly imbalanced normal phase.