Scaling theory of intrinsic Kondo and Hund's rule interactions in magic-angle twisted bilayer graphene

TL;DR

This paper develops a theoretical framework to understand how Kondo and Hund's rule interactions evolve in magic-angle twisted bilayer graphene, revealing their significant impact on electronic phases and Kondo temperature across various fillings.

Contribution

It introduces an analytical renormalization approach for Kondo and Hund's interactions in twisted bilayer graphene, highlighting their influence on Kondo screening and correlated metallic phases.

Findings

Kondo temperature $T_K$ varies strongly with filling and interaction strength.

Kondo screening can occur over a wide range of fractional fillings.

Renormalization of interactions is crucial for understanding experimental phases.

Abstract

Motivated by the recent studies of intrinsic local moments and Kondo-driven phases in magic-angle twisted bilayer graphene, we investigate the renormalization of Kondo coupling ($J_K$) and the competing Hund's rule interaction ($J$) in the low-energy limit. Specifically, we consider a surrogate single-impurity generalized Kondo model and employ the poor man's scaling approach. The scale-dependent $J_K$ and $J$ are derived analytically within the one-loop poor man's scaling approach, and the Kondo temperature ($T_K$) and the characteristic Hund's rule coupling ($J^*$, defined by the renormalized value of $J$ at some small finite energy scale) are estimated over a wide range of filling factors. We find that $T_K$ depends strongly on the filling factors as well as the value of $J_K$. Slightly doping away from integer fillings and/or increasing $J_K$ may substantially enhance $T_K$ in the parameter regime relevant to experiments. $J^*$ is always reduced from the bare value of $J$, but the filling factor dependence is not as significant as it is for $T_K$. Our results suggest that it is essential to incorporate the renormalization of $J_K$ and $J$ in the many-body calculations, and Kondo screening should occur for a wide range of fractional fillings in magic-angle twisted bilayer graphene, implying the existence of Kondo-driven correlated metallic phases. We also point out that the observation of distinct phases at integer fillings in different samples may be due to the variation of $J_K$ in addition to disorder and strain in the experiments.