Symmetry-Resolved Local Density Spectroscopy: Application to Twisted Bilayer Graphene

Abstract

Magic-angle twisted bilayer graphene (MATBG) has been one of the most highly celebrated condensed matter research arenas in recent years, hosting a plethora of exotic phases of matter such as correlated insulators and unconventional superconductivity. To date, however, the nature of the ground state in MATBG remains mysterious despite various theoretical proposals. In this dissertation, we devise a novel symmetry-based approach to diagnose the competing ground state phases of MATBG via local charge-density spectroscopy and verify that the technique can be successfully applied to experimental data. In Chapter 2, we study charge-density patterns arising from the ground states of interacting Bistritzer-Macdonald model. We discover an exotic selection rule which posits the absence of a local feature called the “$\sqrt{3}×\sqrt{3}$ Kekulé pattern” in Kramers Inter-Valley-Coherent (K-IVC) phase at charge neutrality point, which makes it distinct from typical inter-valley coherent phases. In Chapter 3, we define a notion of “local order parameters” for the emergent symmetries in MATBG and develop novel algorithmic techniques which can robustly detect moiré-scale translational and rotational symmetry-breaking from charge-density patterns. We claim that this method allows for a distinction between Time-reversal-symmetric Inter-Valley-Coherent (T-IVC) and Incommensurate Kekulé-Spiral (IKS) phase. In Chapter 4, we stress-test the theoretical predictions made from the previous Chapters by systematically applying the developed techniques to state-of-the-art experimental measurements from scanning-tunneling microscopy. Analysis on experimental data at electron filling $\mu=±2$ confirms signatures consistent with the absence of K-IVC, the presence of IKS at high strain, and the presence of T-IVC at low strain. In conclusion, this dissertation establishes symmetry-resolved local density spectroscopy as a concrete and versatile tool to explore the rich phase diagram of MATBG as well as other moiré materials in the field of twistronics.