Local order parameters and moire translation symmetry breaking of twisted bilayer graphene from local density of states

We develop a method to identify the nature of symmetry breaking in twisted bilayer graphene using atomically-resolved local density of states. We define a set of local order parameters that can be directly extracted from Fourier transform of the local density of states, and show that different theoretical candidate ground states of twisted bilayer graphene shows distinct symmetry breaking features.

In addition to local symmetry breaking, our method can identify symmetry breaking at moire scale. We show knowing the location of graphene lattice sites allows us to characterize whether a given state has moire periodic features or not. We apply this analysis method to the nontrivial example of incommensurate Kekule spiral (IKS), a theoretical candidate state with a special kind of translation breaking, and show that it leaves unambiguous features in LDOS.