Twisted bi-layer graphene: magic range behavior and implications, a first-principles perspective*

The physics of twisted bi-layer and multi-layer graphene continues to be of great interest in understanding strongly correlated electron states, with many details still unclear, and a simple phenomenological model still lacking. The moiré pattern observed experimentally in twisted bilayer graphene (tBLG) clearly shows the formation of different types of domains.  These domains can be explained by the atomic relaxation, both in-plane and out-of-plane, using continuum elasticity theory and the Generalized Stacking Fault Energy (GSFE) concept. Moreover, the atomic relaxation significantly affects the electronic states, leading to a pair of flat bands at the charge neutrality point which are separated by band gaps from the rest. These features appear for a small range of twist angles, that we call the “magic range”, around the twist angle of 1^o. We discuss how all these aspects of the system are crucial for understanding the origin of correlated states and superconductivity in tBLG. We also present a minimal model that can capture these features with 2 flat and 2 auxiliary bands and explore the implications of the model for correlated electron behavior in the context of the Hubbard model.