Classification and Distinction of Possible Insulating Phases in Twisted Bilayer Graphene by Impurity Effects

TL;DR

This paper investigates how impurity effects in twisted bilayer graphene can distinguish between different insulating phases by analyzing local density of states and bound state properties, aiding experimental identification.

Contribution

It introduces a method to classify insulating phases in TBG based on impurity-induced bound states and symmetry considerations, enhancing understanding of phase distinctions.

Findings

Different insulating phases show distinguishable in-gap bound state peaks.

Remaining anti-unitary symmetries classify phases with similar symmetry breaking.

Bound state degeneracy can be detected via STM experiments.

Abstract

In this work the effects of impurity in various insulating phases of the twisted bilayer graphene (TBG) are studied. The well-accepted continuum model\cite{b} is employed and the local density of states (DOS) is calculated. It is found that insulating phases breaking different symmetries proposed in previous theories\cite{pa,op1,Lee_2019} are distinguishable via the number and properties of in-gap bound state peaks induced by impurities in local DOS. Insulating phases breaking the same previously proposed symmetries can be further classified by the remaining anti-unitary symmetries and distinguished by the corresponding remaining Kramers degeneracy of bound states. The in-gap bound state peaks in local DOS and the degeneracy of the bound states can in principle be detected in scanning tunnelling microscopy (STM) experiments, and thus can help to the distinction of various insulating phases.