Numerical Analysis Seminar

Date: September 7, 2022

Time: 2:00PM - 3:00PM

Location: BLOC 302

Speaker: Alexander Watson, University of Minnesota

Title: Moiré-scale PDE models of twisted bilayer graphene

Abstract: 2D materials are materials consisting of a single sheet of atoms. The first 2D material, graphene, a single sheet of carbon atoms, was isolated in 2005. In recent years, attention has shifted to materials created by stacking 2D materials with a relative twist. Such materials are known as moiré materials because of the approximate periodicity of their atomic structures over long distances, known as the moiré pattern. In 2018, experiments showed that, when twisted to the first so-called magic angle (approximately 1 degree), twisted bilayer graphene exhibits exotic quantum phenomena such as superconductivity. I will present the first rigorous justification of the Bistritzer-MacDonald moiré-scale PDE model of twisted bilayer graphene, which played a critical role in identifying twisted bilayer graphene’s magic angles, from a microscopic tight-binding model. If time permits, I will discuss the chiral model, a simplification of the Bistritzer-MacDonald model with a number of remarkable properties.