Aspects of Moiré Quantum Matter

Abstract

The advent of moiré quantum matter has newly unified disparate themes in modern condensed matter physics, chief among them band theory, correlations, and topology. This thesis investigates how the interplay between these foundational elements leads to novel electronic phenomena uniquely enabled by moiré superlattices. We focus on modulated Landau levels, which is one of the simplest settings with all three of band dispersion, correlations and topology, yet is rich enough to capture much of the interesting phenomena of moiré quantum matter. We characterize emergent quantum phases that are newly unlocked by the moiré regime. Specifically, we discuss directional localization, formation of Hall crystals with tunable Chern numbers, and novel fractional Chern insulator collective mode physics in the context of modulated Landau levels. We also show that a class of models comprising itinerant electrons strongly coupled to skyrmion-like magnetic textures, closely connected with moiré transition metal dichalcogenides in which the fractional quantum anomalous Hall effect was observed, can host flat Chern bands, emergent Landau levels, and zero-field non-Abelian topological order. This thesis provides a framework for the study of the essential features of moiré quantum matter and demonstrates how moiré systems provide unprecedented opportunities to explore, design, and manipulate strongly correlated topological quantum matter.