Spectroscopy of Twisted Bilayer Graphene Correlated Insulators

TL;DR

This paper analytically predicts STM signatures of correlated insulating states in twisted bilayer graphene, showing how these signatures can distinguish different ground states and their topological properties.

Contribution

It provides a detailed theoretical analysis of STM signals for various correlated states in TBG, including the impact of valley coupling and Kekule9 distortion, validated against experimental data.

Findings

STM signatures can identify the nature of TBG ground states.

Coupling valleys does not always lead to Kekule9 distortion.

STM signals and Chern numbers can distinguish different correlated insulators.

Abstract

We analytically compute the scanning tunneling microscopy (STM) signatures of integer-filled correlated ground states of the magic angle twisted bilayer graphene (TBG) narrow bands. After experimentally validating the strong-coupling approach at $\pm 4$ electrons/moir\'e unit cell, we consider the spatial features of the STM signal for 14 different many-body correlated states and assess the possibility of Kekul\'e distortion (KD) emerging at the graphene lattice scale. Remarkably, we find that coupling the two opposite graphene valleys in the intervalley-coherent (IVC) TBG insulators does not always result in KD. As an example, we show that the Kramers IVC state and its nonchiral $\mathrm{U} \left( 4 \right)$ rotations do not exhibit any KD, while the time-reversal-symmetric IVC state does. Our results, obtained over a large range of energies and model parameters, show that the STM signal and Chern number of a state can be used to uniquely determine the nature of the TBG ground state.