Re-entrant p-wave superconductivity in a Chern Dartboard Insulator

Abstract

We formulate an exact theory for a 2-band superconductor with inter-orbital pairing and band Hatsugai-Kohmoto (HK) interactions. We apply this theory to a Chern dartboard insulator and compute the pair susceptibility and pair correlations analytically. We find that in the insulating phase previously predicted by BCS theory (small pairing strength $g$, chemical potential $μ$ in the gap), the HK interaction can induce superconductivity, and possibly a Chern dartboard superconductor, by lifting the doubly-occupied band and making it cross the chemical potential. From this HK-induced superconductor, we notice that in a significant parameter range (HK interaction strength $U = 1$, $μ= 0.5$), an insulator-superconductor-insulator re-entrant transition exists. We isolate the re-entrance to a conflation between HK interactions and inter-orbital pairings.