Modelling realistic Hamiltonians for moire lattices

The tight-binding (TB) approximation to the Hamiltonian of the Twisted Bilayer Graphene (TBG) is considered in the Slater-Koster (SK) form. Instead of taking the commonly-accepted parametrization, we generate a new one by fitting the data obtained in the ab-initio Density Functional Based (DFT) calculations. The resulting Hamiltonian is further projected to a smaller twelve-band tight-binding model, giving a systematic way to reduce the dimensionality of the problem. Finally, the localization of the Wannier orbitals and the symmetry of the final Hamiltonian is considered in this work