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

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