Topological Mixed Valence Model for Twisted Bilayer Graphene

Song and Bernevig (SB) have recently proposed a topological heavy fermion description of the physics of magic angle twisted bilayer graphene (MATBG), involving the hybridization of flat band electrons with a relativistic conduction sea. We explore the consequences of this model, seeking a synthesis of understanding drawn from heavy fermion physics and MATBG experiments. We identify a key discrepancy between measured and calculated onsite Coulomb interactions, implicating renormalization effects that are not contained in the current model. With these considerations in mind, we consider an SB model with a single, renormalized onsite interaction between the f-electrons, containing a phenomenological heavy fermion binding potential on the moir\'e AA-sites. This feature allows the simplified model to capture the periodic reset of the chemical potential with filling and the observed stability of local moment behavior. We argue that a two stage Kondo effect will develop in MATBG as a consequence of the relativistic conduction band: Kondo I occurs at high temperatures, establishing a coherent hybridization at the $\Gamma$ points and a non-Fermi liquid of incoherent fermions at the moir\'e K-points; at much low temperatures Kondo II leads to a Fermi liquid in the flat band. Utilizing an auxiliary-rotor approach, we formulate a mean-field treatment of MATBG that captures this physics, describing the evolution of the normal state across a full range of filling factors. By contrasting the relative time-scales of phonons and valence fluctuations in bulk heavy fermion materials with that of MATBG we propose a valley-polaron origin to the Coulomb renormalization and the heavy fermion binding potential identified from experiment. We also discuss the possibility that the two-fluid, non-Fermi liquid physics of the relativistic Kondo lattice is responsible for the strange metal physics observed in MATBG.