A. S. Shankar | Searcharxiv

arXiv2023

Lyapunov exponents in a Sachdev-Ye-Kitaev-type model with population imbalance in the conformal limit and beyond

The Sachdev-Ye-Kitaev (SYK) model shows chaotic behavior with a maximal Lyapunov exponent. In this paper, we investigate the four-point function of a SYK-type model numerically, which gives us access to its Lyapunov exponent. The model consists of two sets of Majorana fermions, called A and B, and the interactions are restricted to being exclusively pairwise between the two sets, not within the sets. We find that the Lyapunov exponent is still maximal at strong coupling. Furthermore, we show that even though the conformal dimensions of the A and B fermions change with the population ratio, the Lyapunov exponent remains constant, not just in the conformal limit where it is maximal, but also in the intermediate and weak coupling regimes.

cond-mat.str-el↗

arXiv2023

Kondo effect in twisted bilayer graphene

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.

cond-mat.str-el↗