Topological Superconductivity in Honeycomb Dirac Systems

There has been a surge of recent interest in superconductivity (SC) in 2D Dirac materials ranging from transition metal dichalcogenides to twisted bilayer graphene. It is important to understand the precise conditions under which one obtains a topological SC state in such systems. We address this question in the simplest honeycomb lattice models that hosts both topological and trivial insulating states in 2D: the Kane-Mele (KM) model for spin-1/2 fermions and the Haldane model for spinless fermions. We describe the results of our extensive self-consistent Bogoliubov-deGennes calculations [1] for these models with a variety of pairing interactions, and show that topological SC states arise only for nearest-neighbor attraction. In the KM model, we find four distinct SC phases, all with finite center-of-mass momentum pairing. Two of these are topological SCs: one a helical spin-triplet SC which is time-reversal invariant and another a chiral spin-triplet SC with Chern number ±1 with equal-spin pairing in one valley and opposite-spin triplet pairing in the other valley. We also discuss possible experimental signatures of these phases.
[1] Lee, Hazra, Randeria and Trivedi, arXiv:1806.08795