Insulator-to-Superconductor Transition in the Kane-Mele Model with Attractive Interactions

We investigate the onset of pairing and the nature of superconducting (SC) states in a Kane-Mele model with attractive interactions. The non-interacting state at half filling evolves from a trivial to a topological insulator as a function of the relative strength of the spin-orbit coupling to the sublattice potential, with a massless Dirac dispersion at the topological transition. At half-filling, there is a finite threshold for superconductivity and we find a particularly rich phase diagram for the case of nearest-neighbor attraction. On either side of the topological transition, we find within mean field theory the same SC state with a condensate that spontaneously breaks translational invariance but is topologically trivial. The insulator-to-superconductor transition is continuous on the topological side and first-order on the trivial side. Near the topological transition, the system is unstable to a different SC state with equal-spin pairing. This state harbors topological superconductivity with a non-trivial Z₂ invariant. Our work illuminates the transitions between topological and trivial insulators and superconductors by capturing all four phases in one model.