Talk by Maciej Zworski
On January 31st, 2024, Maciej Zworski (University of California, Berkeley) gave a talk about "Mathematics of magic angles for twisted bilayer graphene" as part of the research seminar Analysis of the FernUniversität in Hagen. This lecture is partially supported by the COST action Mathematical models for interacting dynamics on networks.
Abstract
Show Abstract
Magic angles refer to a remarkable theoretical (Bistritzer–MacDonald, 2011) and experimental (Jarillo-Herrero et al 2018) discovery, that two sheets of graphene twisted by a certain (magic) angle display unusual electronic properties such as superconductivity.
Mathematically, this is related to having flat bands of nontrivial topology for the corresponding periodic Hamiltonian and their existence be shown for the chiral model of twisted bilayer graphene (Tarnopolsky-Kruchkov-Vishwanath, 2019). A spectral characterization of magic angles (Becker–Embree–Wittsten–Z, 2021, Galkowski–Z, ’23) also produces complex values and the distribution of their reciprocals looks remarkably like a distribution of scattering resonances for a two dimensional problem, with the real magic angles corresponding to anti-bound states. I will review various results on that distribution as well as on the properties of the associated eigenstates.
The talk is based on joint works with S. Becker, M. Embree, J. Galkowski, M. Hitrik, T. Humbert and J. Wittsten.
