Superlattice engineering of topology in massive Dirac fermions
Nishchay Suri, Chong Wang, Benjamin Hunt, Di Xiao
Abstract
We show that a superlattice potential can be employed to engineer topology in massive Dirac fermions in systems such as bilayer graphene, moir\'e graphene-boron nitride, and transition-metal dichalcogenide (TMD) monolayers and bilayers. We use symmetry analysis to analyze band inversions to determine the Chern number $\mathcal{C}$ for the valence band as a function of tunable potential parameters for a class of ${C}_{4}$ and ${C}_{3}$ symmetric potentials. We present a method to engineer Chern number $\mathcal{C}=2$ for the valence band and show that the applied potential at minimum must have a scalar together with a nonscalar periodic part. We discover that certain forms of the superlattice potential, which may be difficult to realize in naturally occurring moir\'e patterns, allow for the possibility of nontrivial topological transitions. These forms may be achievable using an external superlattice potential that can be created using contemporary experimental techniques. Our paper paves the way to realize the quantum spin Hall effect (QSHE), quantum anomalous Hall effect (QAHE), and even exotic non-Abelian anyons in the fractional quantum Hall effect (FQHE).