Theory of Correlated Hofstadter Spectrum in Magic-Angle Graphene

Abstract

The magnetic-field-induced correlated Chern insulator (CCI) states in magic-angle twisted bilayer graphene (MATBG) have been intensively studied in experiments, but a simple and clear understanding of their origin is still lacking. Here, we propose a unified theoretical framework for the CCI states in MATBG that successfully explains most experimental observations. The key insight of our theory is that, due to the very narrow bandwidth of MATBG, correlation-enhanced valley and spin Zeeman terms are critical for shaping the intricate Hofstadter spectrum, resulting in an interwoven, flavor-resolved (spin and valley) Hofstadter spectrum that can well describe the observed CCI states. Crucially, due to the Zeeman effect, the crossings between these flavor-polarized Hofstadter spectra are magnetic-field-dependent, causing certain CCI states to emerge only above a critical field. This is the main mechanism underlying the critical field phenomenon of the CCI states observed in experiments. Our theory provides a clear and unified physical picture for the correlated Hofstadter spectrum in MATBG.