Strong correlations in ABC-stacked trilayer graphene: Moiré is important

Recent experiments on multilayer graphene materials have discovered a plethora of correlated phases, including ferromagnetism and superconductivity, in the absence of a moiré potential. These findings pose an intriguing question of whether an underlying moiré potential plays a key role in determining the phases realizable in tunable two-dimensional quantum materials, or whether it merely acts as a weak periodic potential that perturbs an underlying correlated many body state. In this work, employing a Hartree-Fock mean field analysis, we examine this question theoretically by quantitatively studying the effects of an hexagonal Boron Nitride (h-BN) substrate on ABC-stacked trilayer graphene (ABC-TLG). Our findings highlight the importance of interactions in renormalizing the electronic bandstructure, and the key role played by the moiré potential in determining the strong correlation physics.