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

Abstract

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). For the topologically trivial regime, we find that the moiré potential leads to a strong suppression of the ferromagnetism of the underlying metal. Further, band insulators appear solely at full filling of the moiré unit cell, with a moiré potential stronger than is conventionally assumed. Thus the observed correlated insulating phases in ABC-TLG aligned with h-BN cannot be understood through band folding of the ferromagnetic metal found without the moiré potential. For the topologically non-trivial regime, we discover the appearance of prominent incompressible states when fractional hole fillings (of the moiré unit cell) coincide with the occurrence of fractional-metallic states in the moiré-less setting, as well as a slight weakening of the ferromagnetic nature of the phases; however this once again requires a moiré potential stronger than is conventionally assumed. Our findings highlight the importance of interactions in renormalizing the electronic bandstructure, and emphasizes the key role played by the moiré potential in determining the strong correlation physics.