First-Principles Electronic Structure Investigation of 2D Twisted Bilayers

Since the recent experimental observation of unconventional superconductivity in Twisted Bilayer Graphene (TBG) has brought 2D twisted materials to the front lines of research, there is a need to cover the underlying physics accurately and efficiently. We utilize the first-principles method to calculate both band structures and density of states (DOS) for various sized 2D twisted bilayers of Graphene, BN and MoS₂. Our results reveal that introducing a twist opens a band gap, and Van Hove Singularities are seen symmetric to the dirac point in the DOS. The introduction of a twist angle in graphene also creates a parabolic band dispersion of the dirac cones, normally seen only in Bernal stacked graphene on account of strong stability and interlayer correlation. We evaluate the contribution of cell size to band structure by enlarging the unit cell from 2×2 to 12×12. The electronic properties of the smaller cell remains constant as the cell size increases. Furthermore, we treat a non-periodic 2D twisted bilayer by introducing a vacuum, from which we can draw parallels between the electronic structures and reveal the deep underlying physics.