Maciej Zworski (Berkeley)
Magic angles for a model of twisted bilayer graphene
Abstract:
Magic angles are a hot topic in condensed matter physics:
when two sheets of graphene are twisted by those angles the resulting
material is superconducting. I will present a very simple operator
whose spectral properties are thought to determine which angles are
magical. It comes from a 2019 PR Letter by
Tarnopolsky--Kruchkov--Vishwanath. The mathematics behind this is an
elementary blend of representation theory (of the Heisenberg group in
characteristic three), Jacobi theta functions and spectral instability
of non-self-adjoint operators (involving Hörmander's bracket condition
in a very simple setting). Recent mathematical progress also includes
the proof of existence of generalized magic angles and computer
assisted proofs of existence of real ones (Luskin--Watson, 2021). The
results will be illustrated by colourful numerics which suggest many
open problems (joint work with S Becker, M Embree and J Wittsten,
2020).