Superfluid transition in the attractive Hofstadter-Hubbard model

TL;DR

This paper investigates the superfluid transition in a Fermi gas on a square lattice under a magnetic field, using a mean-field approach that accounts for the complex Hofstadter spectrum.

Contribution

It introduces a generalized pairing equation considering the multi-band Hofstadter spectrum and analyzes the effects of various parameters on the superfluid transition boundary.

Findings

Superfluid transition boundary depends on magnetic flux and interaction strength.

Density of states significantly influences pairing and transition.

Center-of-mass momentum of Cooper pairs affects superfluid properties.

Abstract

We consider a Fermi gas that is loaded onto a square optical lattice and subjected to a perpendicular artificial magnetic field, and determine its superfluid transition boundary by adopting a BCS-like mean-field approach in momentum space. The multi-band structure of the single-particle Hofstadter spectrum is taken explicitly into account while deriving a generalized pairing equation. We present the numerical solutions as functions of the artificial magnetic flux, interaction strength, Zeeman field, chemical potential, and temperature, with a special emphasis on the roles played by the density of single-particle states and center-of-mass momentum of Cooper pairs.