Topological Superconductivity on Moire Superlattices

Surprising correlated phenomena such as superconductor and insulator at fractional electron fillings have been observed in systems with Moire superlattice. We study the nature of these correlated phenomena, and explore the possibility of topological superconductivity in these systems using different approaches. The Dirac valley degree of freedom allows these system to form either spin triplet or spin singlet topological superconductor, depending on the sign of an effective "Hund's coupling". Experimental predictions such as magnetic flux quantization can be made based on the particular type of pairing. We will also investigate the nature of the observed insulators, and map the effective spin-valley physics of the insulator at both 1/2 and 1/4 filling to the boundary of a higher dimensional symmetry protected topological (SPT) state. The spin-valley physics of the insulators is governed by a Lieb-Shultz-Mattis theorem which can be interpreted as the boundary 't Hooft anomaly of the higher dimensional SPT state.