Stability of superconducting phases in the Haldane model

The breaking of time reversal symmetry generally suppresses superconductivity through orbital or, for spin-singlet pairing, paramagnetic limiting. The recent observation of superconductivity emerging in a phase showing an anomalous Hall effect potentially due to a flux phase, such as in the kagome superconductors of the AV3Sb5 (A = K, Rb, Cs) family, thus raises the question, what pairing channels are robust against this kind of time-reversal-symmetry breaking. To investigate this question, we study different pairing channels and their stability as a funciton of flux within the massless Haldane model, which shows an anomalous Hall effect for generic filling. We study pairing channels stemming from on-site, nearest-, and next-to-nearest-neighbor interactions and find that most pairing channels only weekly depend on the staggered flux. Finally, we study the temperature dependence of the thermal Hall conductivity as a possible signature of the different pairing channels.