# Two-dimensional imbalanced Fermi gas in antiparallel magnetic fields

## TL;DR

This paper investigates a two-dimensional imbalanced Fermi gas under antiparallel synthetic magnetic fields, revealing complex phase structures including superfluid, Fulde-Ferrell, and quantum Hall phases through analytical and numerical methods.

## Contribution

It provides the first detailed phase diagram of an imbalanced 2D Fermi gas with antiparallel magnetic fields, highlighting the stability of Fulde-Ferrell states and phase transitions.

## Key findings

- Fulde-Ferrell state is favored over Larkin-Ovchinnikov in weak coupling.
- Rich phase diagram with quantum Hall insulator, superfluid, and Fulde-Ferrell phases.
- Multiple first- and second-order quantum phase transitions identified.

## Abstract

We study a two-dimensional Fermi gas with an attractive interaction subjected to synthetic magnetic fields, which are assumed to be mutually antiparallel for two different spin components with population imbalance. By employing the mean-field approximation, we show that the Fulde-Ferrell state is energetically favored over the Larkin-Ovchinnikov state in the weak-coupling limit. We then elucidate the zero-temperature phase diagram in the space of attraction and two chemical potentials analytically at weak coupling as well as numerically beyond it. Rich structures consisting of quantum Hall insulator, unpolarized superfluid, and Fulde-Ferrell phases separated by various second-order and first-order quantum phase transitions are found.