Two Silhouettes of Strongly Correlated Topological Phases: Fractionalization and Crystallization

Abstract

Recent advances in two-dimensional materials have unveiled a plethora possibilities for exploring strongly correlated topological phases. This thesis focuses on predicting novel topological phases and examining their properties. Chapters 1 and 2 discuss phases characterized by fractionalization, where the system's excitations exhibit fractional electric charges. These phases, though arising without external magnetic fields, closely resemble fractional quantum Hall phases typically induced by strong magnetic fields. Specifically, Chapter 1 investigates fractional and integer Chern insulator phases within higher Chern bands that were proposed to exist in twisted graphene systems. Chapter 2 reports predictions of a composite Fermi liquid phase in twisted MoTe2 through numerical simulations. Chapters 3 through 6 explore scenarios where electrons crystallization coexists with band topology. Contrary to the conventional belief that electronic crystals are topologically trivial, we propose that anomalous Hall crystals — topologically nontrivial electronic crystals — can exist. Chapter 3 demonstrates how the concept of anomalous Hall crystals can explain recent experimental findings in rhombohedral graphene moiré systems. Chapter 4 introduces a simplified theoretical model elucidating the origin of Chern numbers associated with these anomalous Hall crystals. Chapter 5 proposes a minimal model of the anomalous Hall crystal, bridging it to previous models of electronic crystallization. Finally, Chapter 6 investigates the elastic theory and phonon dynamics in electron crystals in the presence of Berry curvature.