RKKY interactions and Hund's rule in twisted bilayer graphene

Twisted bilayer graphene (TBG) has shown two seemingly contradictory characters: (1) quantum-dot-like behavior in STM indicates that then electrons are localized; (2) the transport experiments suggest the itinerant character. Two features can both be captured by a topological heavy-fermion model as demonstrated in Ref. [1]. In this work, based on the Schrieffer-Wolff transformation and the Anderson lattice model defined in Ref. [1], we provide a Kondo-model description of the TBG. In the resulting model, the conduction electrons interact with U(4) local moments via a superexchange and the Hund’s interactions. We calculate the RKKY interactions between U(4) moments induced by these two couplings. By analyzing the behavior of the RKKY interactions, we prove Hund’s rule of the ground state, namely, the wave function tends to be symmetric under permutation of the flavor indices [1].

[1] Z. Song, B. A. Bernevig, Phys. Rev. Lett. 129, 047601 (2022).