We introduce a minimum tight-binding model with only three parameters extracted from graphene and untwisted bilayer graphene. This model reproduces quantitatively the electronic structure of not only these two systems and bulk graphite near the Fermi level, but also that of twisted bilayer graphene including the value of the magic angle, at which bands at EF flatten without overlap and two gaps open, one above and one below EF. The Hamiltonian is sufficiently transparent and flexible to be adopted to other twisted layered systems.
@article{arxiv.1808.03634,
title = {Minimum model for the electronic structure of twisted bilayer graphene and related structures},
author = {Xianqing Lin and David Tománek},
journal= {arXiv preprint arXiv:1808.03634},
year = {2018}
}