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 multiband butterfly spectrum explicitly into account, it unveils how dramatically the interband contribution to the phase stiffness dominates the intraband one with an increasing interaction strength for any given magnetic flux.

Figure 1

The critical SF transition temperature $k_B{T}_{\text{BKT}}/t$ is shown in the first row together with the corresponding SF order parameter $\mathrm{\Delta }/t$ in the second row, the relative weight of the intraband and interband contributions to the phase stiffness $(D_0^{\mathrm{intra}}-D_0^{\mathrm{inter}})/D_0$ in the third row, and the condensate fraction $F_c/F$ in the bottom row.

Figure 2

The critical SF transition temperature $k_B{T}_{\text{BKT}}/t$ is shown in the first row together with the corresponding SF order parameter $\mathrm{\Delta }/t$ in the second row, the relative weight of the intraband and interband contributions to the phase stiffness $(D_0^{\mathrm{intra}}-D_0^{\mathrm{inter}})/D_0$ in the third row, and the condensate fraction $F_c/F$ in the bottom row.

Figure 3

The critical SF transition temperature $k_B{T}_{\text{BKT}}/t$ is shown in the first row together with the corresponding SF order parameter $\mathrm{\Delta }/t$ in the second row and the condensate fraction $F_c/F$ in the bottom row.