Topological Mixed Valence Model for Twisted Bilayer Graphene
Liam L. H. Lau, Piers Coleman
Abstract
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. Here, we explore the consequences of this model, seeking a synthesis of understanding drawn from heavy-fermion physics and MATBG experiments. Our work identifies a key discrepancy between measured and calculated on-site Coulomb interactions, implicating renormalization effects that are not contained in the current model. With these considerations in mind, we consider a SB model with a single, renormalized on-site interaction between the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>f</a:mi> </a:math> electrons, containing a phenomenological heavy-fermion binding potential on the moiré <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>A</c:mi> <c:mi>A</c:mi> </c:math> 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 <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi mathvariant="normal">Γ</e:mi> </e:math> points and a non-Fermi liquid of incoherent fermions at the moiré <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"> <h:mi>K</h:mi> </h:math> points; at much lower 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 timescales of phonons and valence fluctuations in bulk heavy-fermion materials with that of MATBG, we are led to 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.