EVENT DETAILS AND ABSTRACT

Title: Twisted bilayer graphene and complex line bundles
Speaker: Maciej Zworski
Speaker Info: Berkeley
Brief Description:
Special Note: Note unusual day, time
Abstract:

I will present recent work with S Becker and T Humbert on magic angles for the chiral model of the twisted bilayer graphene. These are angles at which the Bloch-Floquet bands are completely flat at zero energy. In earlier work (with S Becker, M Embree and J Wittsten) we provided a spectral characterization of these angles and connected it to the theta function picture in the physics literature (Tarnopolsky--Kruchkov--Vishwanath). Now we show that there are infinitely (possibly complex) magic angles and analyse the corresponding Bloch-Floquet eigenfunctions (including in ongoing work with M Hitrik on their exponential decay). I will also describe the connection to the topology of complex line bundles of eigenfunctions and introduce some open problems.