Origin of flat bands and topology in twisted transition metal dichalcogenides homobilayers.

We explore the chiral limit of massive Dirac field theories applicable to moire materials and uncover the similar origin of flat bands in both twisted bilayer graphene and twisted transition metal dichalcogenides (TMD) homobilayers. We find that the non-trivial topology of the flat bands is due to a layer-orbit coupling, the analog of spin-orbit coupling for relativistic Dirac fermions, which is non-perturbative on the moire scale, and allows for the flat bands to be exactly flat. We compare the flat band in moire TMDs to the Landau levels of a TMD monolayer under a magnetic field, and discuss the remarkable robustness of the flat bands to certain types of disorder.