Bryan Li L&S Math & Physical Sciences
Band Crossings in Twisted Multilayer Graphene
My project focuses on analysis of mathematical models of twisted multilayer graphene (TMG), which is a material arising from stacking multiple layers of graphene together, which exhibits many special electronic properties at certain angles, including superconductivity. When there are two layers, this is called twisted bilayer graphene (TBG), and this material has been studied extensively both experimentally and mathematically. However, less is known about TMG.
Mathematically, the behavior of TBG and TMG are determined by the “electronic bands” (see Fig. 1). In certain kinds of even-layered TMG, there are points at which the bands “cross,” and my project aims to understand the shape of the bands near the crossings. This shape is always a cone in TBG, but for 4 layers it could be either a double-cone or a paraboloid. Less is known when there are 6 or more layers, and the goal for my project is to determine mathematically which kinds of crossings are possible for higher numbers of layers, and also determine mathematical criteria for the angles that result in each of those possibilities.
Message To Sponsor
Thank you for supporting my research this summer! I am excited to work on this project over the summer because it deals with areas of math that I really enjoy (PDE, functional analysis, and mathematical physics). I also am grateful for the opportunity to obtain research experience before graduate school.