Network of chiral one-dimensional channels and localized states emerging in a moiré system

Abstract

Moiré systems provide a highly tunable platform for engineering band structures and exotic correlated phases. Here, we theoretically study a model for a single layer of graphene subject to a smooth moiré electrostatic potential, induced by an insulating substrate layer. For sufficiently large moiré unit cells, we find that ultra-flat bands coexist with a triangular network of chiral one-dimensional (1D) channels. These channels mediate an effective interaction between localized modes with spin-, orbital- and valley degrees of freedom emerging from the flat bands. The form of the interaction reflects the chirality and 1D nature of the network. We study this interacting model within an SU(4) mean-field theory, semi-classical Monte-Carlo simulations, and an SU(4) spin-wave theory, focusing on commensurate order stabilized by local two-site and chiral three-site interactions. By tuning a gate voltage, one can trigger a non-coplanar phase characterized by a peculiar coexistence of three different types of order: ferromagnetic spin order in one valley, non-coplanar chiral spin order in the other valley, and 120∘ order in the remaining spin and valley-mixed degrees of freedom. Quantum and classical fluctuations have qualitatively different effects on the observed phases and can, for example, create a finite spin-chirality purely via fluctuation effects.