Band structure theory of twisted bilayer graphene

Twisted bilayer graphene show various interlayer interaction under different rotation angles, which make the system presents nontrivial physical properties, such as unconventional quantum hall effect and berry's phase, correlated insulator behaviour and unconventional superconductivity in magic angle graphene superlattice, et al. However, when the rotation angle is small, the electronic structure, such as band, can't be simulated by the first-principles method. In this project, combine tight-binding method and first-principles simulation, we construct interlayer Hamiltonian matrix element and improve the effective continuum model in band structure theory. Based on this, we construct the wavefunction of each layer in superlattice and then build the Hamiltonian matrix, which further simplify the band structure theory model. Finally, we extend this model to other 2D bilayer systems. The success implementation of this project will construct a simple, cheap and general method for band structure simulation of twisted bilayer graphene, and provide a useful tool for the relative physical effects study of 2D bilayer materials.