Probing strong correlation and discriminating insulating phases in twisted bilayer graphene through scanning tunneling microscopy

At integer fillings, the quenched kinetic energy in twisted bilayer graphene (TBG) at the magic angle induces a wealth of correlated insulators. For a large manifold of insulating ground states, the exact many-body charge-one excitations can be computed analytically. This gives direct access to the corresponding spectral function (SF) - the key quantity measured in scanning tunneling microscopy. We derive the fully-interacting TBG SF at ±4 electrons/moiré unit cell (where the nature of the ground state is unambiguous) and experimentally validate our approach, finding evidence of strong correlations. For all other integer fillings, we consider the spatial features of the corresponding SFs and assess the possibility of Kekulé distortion (KD) emerging at the graphene lattice scale. Remarkably, we find that coupling the two graphene valleys in the intervalley-coherent TBG insulators does not always result in KD. For instance, we show that the K-IVC state and its nonchiral U(4) rotations do not exhibit any KD. Consequently, we argue that the presence or absence of KD can be used to discriminate the various TBG insulators.