Novel electrical properties of moiré graphene systems

In this review, we discuss the electronic structures, topological properties, correlated states, nonlinear optical responses, as well as phonon and electron-phonon coupling effects of moiré graphene superlattices. First, we illustrate that topologically non-trivial flat bands and moiré orbital magnetism are ubiquitous in various twisted graphene systems. In particular, the topological flat bands of magic-angle twisted bilayer graphene can be explained from a zeroth pseudo-Landau-level picture, which can naturally explain the experimentally observed quantum anomalous Hall effect and some of the other correlated states. These topologically nontrivial flat bands may lead to nearly quantized piezoelectric response, which can be used to directly probe the valley Chern numbers in these moiré graphene systems. A simple and general chiral decomposition rule is reviewed and discussed, which can be used to predict the low-energy band dispersions of generic twisted multilayer graphene system and alternating twisted multilayer graphene system. This review further discusses nontrivial interaction effects of magic-angle TBG such as the correlated insulator states, density wave states, cascade transitions, and nematic states, and proposes nonlinear optical measurement as an experimental probe to distinguish the different “featureless” correlated states. The phonon properties and electron-phonon coupling effects are also briefly reviewed. The novel physics emerging from band-aligned graphene-insulator heterostructres is also discussed in this review. In the end, we make a summary and an outlook about the novel physical properties of moiré superlattices based on two-dimensional materials.