Spectroscopy of Twisted Bilayer Graphene Correlated Insulators

We calculate STM signatures of correlated ground-states at integer filling of the magic angle twisted bilayer graphene narrow bands. First, we compute the fully-interacting TBG spectral function at $\pm 4$ electrons/moir\'e unit cell and show that it can be used to experimentally validate the strong-coupling approach. Although variation exists in the data, we find experimental evidence for the strong-coupling regime. For all other integer fillings of the flat bands, we consider the spatial features of the corresponding spectral functions of many states in the large degenerate ground-state manifold, and assess the possibility of Kekul\'e distortion (KD) emerging at the graphene lattice scale. Remarkably, we find that coupling the two opposite graphene valleys in the intervalley-coherent (IVC) TBG insulators does not always result in KD. As an example, we show that the K-IVC state and its nonchiral $\mathrm{U} \left( 4 \right)$ rotations do not exhibit any KD, while T-IVC does. We analyze 14 different many-body correlated states and show that their combined STM/Chern number signal can be used to uniquely determine the nature of the many-body ground-state. Their STM signal and features are obtained over a large range of energies and model parameters.