Topological bands and correlated states in helical trilayer graphene

Abstract

The intrinsic anomalous Hall effect (AHE) is driven by non-zero Berry curvature and spontaneous time-reversal symmetry breaking. This effect can be realized in two-dimensional moiré systems hosting flat electronic bands but is not usually seen in inversion-symmetric materials. Here, we show that this physics is manifested in helical trilayer graphene—three graphene layers, each twisted in sequence by the same angle—although the system retains global in-plane inversion symmetry. We uncover a phase diagram of correlated and magnetic states at a magic twist angle of 1.8∘, which is explained by a lattice relaxation that leads to the formation of large periodic domains where in-plane inversion symmetry is broken on the moiré scale. Each domain harbours flat topological bands with opposite Chern numbers in the two valleys. We find correlated states at multiple integer and fractional electron fillings per moiré unit cell and an AHE at a subset of them. The AHE disappears above a critical electric displacement field at one electron per unit cell, indicating a topological phase transition. We establish helical trilayer graphene as a platform that presents an opportunity to engineer topology due to its emergent moiré-scale symmetries. Trilayer graphene with the layers consecutively twisted by the same angle is shown to be a platform in which correlated and topological states exist, driven by local lattice relaxations.