Dynamical correlations and order in twisted bilayer graphene

Dynamical correlations and long-range order both play a crucial role in shaping the low-temperature phase diagram of magic-angle twisted bilayer graphene. We use dynamical mean-field theory (DMFT) on the topological heavy Fermion model of twisted bilayer graphene—with and without symmetry-breaking—to study this interplay in the absence of strain. We find that a host of puzzling experimental observations from transport, thermodynamic, and spectroscopic experiments are explained by three central phenomena: (i) the formation of local spin and valley isospin moments, (ii) the ordering of these moments around 10K, and (iii) a cascadic redistribution of charge between light and heavy carriers upon doping. At integer fillings, there is a depletion of spectral weight in the symmetric state, and robust insulating gaps in the ordered phases. Upon doping away from integer fillings, we find an insulator-to-metal transition into a bad (good) metal above (below) the ordering temperature. This order-facilitated coherence is the microscopic mechanism behind the observed isospin Pomeranchuk effect. Further doping induces charge transfer such that, once between neighbouring integer fillings, light carriers are emptied and heavy carriers are populated. The charge reshuffling is associated with doping-induced Lifshitz transitions and variations of the electronic compressibility ranging from nearly incompressible to negative. Our findings highlight the essential role of charge transfer, hybridization and ordering in shaping the electronic excitations and thermodynamic properties in twisted bilayer graphene.