Strongly interacting electrons in Sachdev-Ye-Kitaev models and twisted bilayer graphene

Abstract

In this thesis, we study systems of electrons in which strong correlations give rise to emergent exotic physics. The first part of the thesis focuses on extensions to the topical Sachdev-Ye-Kitaev (SYK) model of a non-fermi liquid. Firstly, the chaotic nature of the bipartite SYK model is studied by a calculation of its Lyapunov exponent at intermediate and strong coupling. Next, a coupled Yukawa SYK model is used to understand the holographic duality between a strongly coupled superconducting Josephson junction and a wormhole in anti de Sitter space. The second part of the thesis addresses possible experimental consequences of the emergent strong correlations at a higher order van Hove singularity in the band structure of magic angle twisted bilayer graphene, and suggests that it may be probed through the Kondo response of a magnetic impurity embedded on its surface.