Berezinskii-Kosterlitz-Thouless transition in the time-reversal-symmetric Hofstadter-Hubbard model

Assuming that two-component Fermi gases with opposite artificial magnetic fields on a square optical lattice are well-described by the so-called time-reversal-symmetric Hofstadter-Hubbard model, we explore the thermal superfluid properties along with the critical Berezinskii-Kosterlitz-Thouless (BKT) transition temperature in this model over a wide-range of its parameters. In particular, since our self-consistent BCS-BKT approach takes the multi-band butterfly spectrum explicitly into account, it unveils how dramatically the inter-band contribution to the phase stiffness dominates the intra-band one with an increasing interaction strength for any given magnetic flux.