Recovery of massless Dirac fermions at charge neutrality in strongly interacting twisted bilayer graphene with disorder

Stacking two graphene layers twisted by the `magic angle' generates flat energy bands, which in turn catalyzes various strongly correlated phenomena. At charge neutrality, transport measurements reveal superficially mundane semimetallicity in some samples yet robust insulation in others. We propose that the interplay between interactions and disorder admits either behavior, even when the system is strongly correlated and locally gapped. We argue that strong interactions supplemented by weak, smooth disorder stabilize a network of gapped quantum valley Hall domains with spatially varying Chern numbers determined by the disorder landscape --- even when an entirely different order is favored in the clean limit. Sufficiently small samples that realize a single domain are insulating. Conversely, multi-domain samples exhibit re-emergent massless Dirac fermions formed by gapless domain-wall modes, yielding semimetallic behavior. Our results highlight the crucial role that randomness can play in ground-state selection. We discuss experimental tests of our proposal.