Speakers: Tal Malinovitch (Rice University)

Title: Twisted Bilayer Graphene in Commensurate Angles

Abstract: Graphene is an exciting new two-dimensional material. Though it was considered theoretical for a long time, it was isolated about 20 years ago. Since then, it has drawn much attention due to its numerous exciting properties. More recently, it was discovered that when twisting two layers of graphene with respect to each other, at certain angles called ``magic angles", exotic transport properties emerge. The primary tool for studying this thus far is the famous Bistritzer-MacDonald model, which relies on several approximations. 

This work aims to build the first steps in studying magic angles without using this model. Thus, we study a model for TBG without the approximations mentioned above in the continuum setting, using two copies of potential with the symmetries of graphene, sharing a common origin and twisted with respect to each other (so-called TBG in AA stacking). We describe the angles for which the two twisted lattices are commensurate and prove the existence of Dirac cones for such angles. Furthermore, we show that for small potentials, the slope of the Dirac cones is small for commensurate angles that are close to incommensurate angles. This work is the first in a series of works to build a more fundamental understanding of the phenomenon of magic angles. 
In this talk, I will introduce the main phenomena of twisted bilayer graphene and state our main results.