Student Harmonic Analysis and PDE Seminar (HADES): Introduction to the mathematics of graphene

Seminar | October 30 | 3:40-5 p.m. | 740 Evans Hall

 Maciej Zworski, UC Berkeley

 Department of Mathematics

We will consider the simplest model of graphene given by a hexagonal quantum graph and explain the appearance of the famous "Dirac points". All the relevant concepts, quantum graphs, density of states etc, will be explained from scratch. When the magnetic field is added interesting oscillations appear in physically observed quantities. Using semiclassical methods (with the strength of the magnetic field as the small parameter) we will give a geometric description of the density of states. This description will then be used to see magnetic oscillations such as the de Haas–van Alphen effect. Numerical example will also be presented. Joint work with S Becker.