Pairing and Vortex Lattices for Interacting Fermions in Optical Lattices with a Large Magnetic Field

TL;DR

This paper investigates the vortex lattice structures and pairing mechanisms of interacting fermions in optical lattices under strong magnetic fields, revealing phase transitions and the influence of magnetic translation symmetry.

Contribution

It introduces a self-consistent mean-field approach to determine vortex lattice configurations and analyzes phase transitions in fermionic systems with magnetic flux.

Findings

Vortex lattice structures depend on flux density.

Phase transition from Hofstadter insulator to superfluid.

Magnetic translation symmetry influences wave function degeneracy.

Abstract

We study the structure of pairing order parameter for spin-1/2 fermions with attractive interactions in a square lattice under a uniform magnetic field. Because the magnetic translation symmetry gives a unique degeneracy in the single-particle spectrum, the wave function has both zero and finite momentum components co-existing, and their relative phases are determined by a self-consistent mean-field theory. We present a microscopic calculation that can determine the vortex lattice structure in the superfluid phase for different flux densities. Phase transition from a Hofstadter insulator to a superfluid phase is also discussed.