Electron Crystallization in the Topological Bands of Multilayer Graphene Heterostructures

Recent discoveries of integer quantum anomalous Hall (IQAH) effects in multilayer graphene heterostructures have raised a number of questions about the role of interactions and band topology in electronic fluids. In this talk, I will discuss how these observations can be understood from the perspective of topological variants of the famous Wigner crystal, where translational symmetry is broken and an accompanying Hall response emerges. I will first provide a microscopic understanding and phenomenological crystal interpretation of the observed IQAH integer at filling \nu = 1 and discuss its stability in two-dimensional platforms. I will then discuss two possible interpretations of the “extended” IQAH state, which persists over a range of densities, in terms of anomalous Hall crystals (AHCs) and a “two-component” electronic crystal consisting of a hole crystal doped on top of the \nu = 1 state. I will discuss the current-driven transport properties and phase transitions associated with these crystals. Finally, I will discuss some generic elastic properties of AHCs in the context of toy models and in multilayer graphene, and contrast their mechanical properties with those of the canonical Wigner crystal.