Kondo effect in twisted bilayer graphene

Abstract

The emergence of flat bands in twisted bilayer graphene at the magic angle can be understood in terms of a vanishing Fermi velocity of the Dirac cone. This is associated with van Hove singularities approaching the Fermi energy and becoming higher-order. In the density of states this is reflected by flanking logarithmic van Hove divergences pinching off the central Dirac cone in energy space. The low-energy pseudogap of the Dirac cone away from the magic angle is replaced by a power-law divergence due to the higher-order van Hove singularity at the magic angle. This plays an important role in the exotic phenomena observed in this material, such as superconductivity and magnetism, by amplifying electronic correlation effects. Here we investigate one such correlation effect -- the Kondo effect due to a magnetic impurity embedded in twisted bilayer graphene. We use the Bistritzer-MacDonald model to extract the low-energy density of states of the material as a function of twist angle, and study the resulting quantum impurity physics using perturbative and numerical renormalization group methods. Although at zero temperature the impurity is only Kondo screened precisely at the magic angle, we find highly nontrivial behavior at finite temperatures relevant to experiment, due to the complex interplay between Dirac, van Hove, and Kondo physics.

arXiv comment16 pages, 8 figures

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• High-order Van Hove singularities and their connection to flat bands
• Moiré optical phonons dancing with heavy electrons in magic-angle twisted bilayer graphene
• Scaling theory of intrinsic Kondo and Hund's rule interactions in magic-angle twisted bilayer graphene
• Pair-density-wave and $s\pm \mathrm{i}d$ superconductivity in a strongly coupled, lightly doped Kondo insulator
• Non-Hermitian Numerical Renormalization Group: Solution of the non-Hermitian Kondo model
• Vacancy-induced tunable Kondo effect in twisted bilayer graphene
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• Kondo effect in a two-dimensional electron gas in the Persistent Spin Helix regime