Hofstadter-Hubbard model with opposite magnetic fields: Bardeen-Cooper-Schrieffer pairing and superfluidity in the nearly flat butterfly bands

TL;DR

This paper investigates superfluidity in the Hofstadter-Hubbard model with opposite magnetic fields, revealing unique properties of nearly-flat butterfly bands using BCS mean-field theory, including order parameters and transition temperatures.

Contribution

It introduces a BCS mean-field approach to analyze superfluidity in the Hofstadter-Hubbard model with nearly-flat butterfly bands, highlighting novel superfluid properties.

Findings

Superfluid properties are well-described by a single uniform order parameter.

Unusual superfluid behavior observed in ground state and finite temperatures.

Critical BCS and BKT transition temperatures are characterized.

Abstract

Despite the multi-band spectrum of the widely-known Hofstadter butterfly, it turns out that the pairing correlations of the time-reversal-symmetric Hofstadter-Hubbard model are well-described by a single order parameter that is uniform in real space. By exploiting a BCS mean-field theory for the nearly-flat butterfly-bands regime of low magnetic-flux limit, here we reveal a number of unusual superfluid properties both in the ground state and at finite temperatures. Our thorough analysis includes but is not limited to the order parameter, condensate and superfluid fractions, and the critical BCS and BKT transition temperatures.