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

Moire 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 moire electrostatic potential, induced by an insulating substrate layer. For sufficiently large moire 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(& LCIRC;) 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.

Automated summary

Moire systems provide a highly tunable platform for engineering band structures and exotic correlated phases. A theoretical study of a single layer of graphene subject to a smooth moire electrostatic potential is conducted, and it is found that ultra-flat bands coexist with a triangular network of chiral one-dimensional channels. Effective interactions between localized modes with multiple degrees of freedom emerge from the flat bands, and the form of these interactions reflects the chirality and one-dimensional nature of the network. The study focuses on commensurate order stabilized by local two-site and chiral three-site interactions and explores the effects of quantum and classical fluctuations on the observed phases.