Simulation of the electronic band structure of twisted bilayer graphene using the tight-binding model

Abstract

This senior project presents a model for calculating the band structure of twisted bilayer graphene for large and small twist angles using the tightbinding model. We also provide the program used for the calculations written on MATLAB 2018b. For large twist angles, we follow the model of A. O. Sboychakov. For small twist angles, we follow the model of A. H. Mac- Donald. We found that the magic angle, which yields minimum bandwidth, is equal to 1.05 degree which is agree with MacDonald’s model and the density of states of twisted bilayer graphene at the magic angle is very high near the Fermi energy which suggests that the superconducting state can be obtained with the right conditions. Our model also shows that there are energy gaps on both sides of Fermi energy which means the insulating state of twisted bilayer graphene may be obtainable.