Vacancy-induced tunable Kondo effect in twisted bilayer graphene

In single sheets of graphene, vacancy-induced states have been shown to host an effective spin-1/2 hole that can be Kondo-screened at low temperatures. In this study, we show how these vacancy-induced impurity states survive in twisted bilayer graphene (TBG), which thus provides a tunable system to probe the critical destruction of the Kondo effect in pseudogap hosts. An atomic-scale model combined with ab initio calculations is used to determine the nature of the vacancy states in the vicinity of the magic angle in TBG, demonstrating that the vacancy can be treated as a quantum impurity. Utilizing this insight, we construct an Anderson impurity model with a TBG host that we solve using the numerical renormalization group combined with the kernel polynomial method. We determine the phase diagram of the model and show how there is a strict dichotomy between vacancies in AA/BB versus AB/BA tunneling regions. In AB/BA vacancies, we find that the Kondo temperature at the magic angle develops a broad distribution with a tail to vanishing temperatures due to multifractal wavefunctions at the magic angle. We argue that the scanning tunneling microscopy response in the vicinity of the vacancy can act as a non-trivial probe of both the critical single-particle states and the underlying many-body ground state in magic-angle TBG.