Strong correlations in ABC-stacked trilayer graphene: Moir\'{e} is important

TL;DR

This study uses Hartree-Fock analysis to show that moiré potentials significantly influence correlated phases in ABC-stacked trilayer graphene, affecting ferromagnetism and insulating states, and highlighting the importance of interactions and moiré effects.

Contribution

The paper demonstrates that strong moiré potentials are essential to explain correlated insulating phases and magnetic properties in ABC-stacked trilayer graphene aligned with h-BN.

Findings

Moiré potential suppresses ferromagnetism in the trivial regime.

Band insulators appear only at full moiré unit cell filling with strong moiré potential.

In the non-trivial regime, fractional fillings lead to incompressible states and weakened ferromagnetism.

Abstract

Recent experiments on multilayer graphene materials have discovered a plethora of correlated phases, including ferromagnetism and superconductivity, in the absence of a moir\'{e} potential. These findings pose an intriguing question of whether an underlying moir\'{e} 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 moir\'{e} potential leads to a strong suppression of the ferromagnetism of the underlying metal. Further, band insulators appear solely at full filling of the moir\'{e} unit cell, with a moir\'{e} 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 moir\'{e} potential. For the topologically non-trivial regime, we discover the appearance of prominent incompressible states when fractional hole fillings (of the moir\'{e} unit cell) coincide with the occurrence of fractional-metallic states in the moir\'{e}-less setting, as well as a slight weakening of the ferromagnetic nature of the phases; however this once again requires a moir\'{e} 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 moir\'{e} potential in determining the strong correlation physics.