Ground state properties of twisted multilayer graphene

Multi-layer Moiré materials offer a tunable platform for realizing electronic systems with strong electron correlations and topologically nontrivial states. We focus here on magic angle twisted bilayer and trilayer graphene, each exhibiting a flat band around the Fermi energy. In this work we determine the electronic properties of both platforms using an ab initio based, multi-million atomistic p_z tight-binding model [1]. The electron-electron interactions are accounted for on the mean field level, using self-consistent Hartree-Fock (HF) method and realistic Coulomb matrix elements. The HF orbitals are obtained by expanding them in Bloch function for each sublattice containing a carbon atom in a unit cell and diagonalising the large Hamiltonian matrix for each allowed wavevector self-consistently. This enables us to determine the magnetic and topological properties of these systems as a function of the filling factor, interaction strength, vertical electric field and presence of an hBN substrate. From Berry curvature of HF orbitals we determine plausible conditions for the system to exhibit integer and fractional topological phases [2] and compare the bilayer and tri-layer results.