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

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