The GW approximation in magic-angle twisted bilayer graphene

A generalized form of ferromagnetism in which spin is replaced by spin×valley flavor degrees of freedom is a prominent part of the physics of magic-angle twisted bilayer graphene (MATBG). The MATBG flat band octet consists of a single valence band and a single conduction band for four different flavors.  We report on a semi-quantitative theory of flavor ferromagnetism in MATBG based on a realistic band structure model and a one-shot GW approximation for the dependence of the exchange-correlation energy on flavor-dependent filling factors ν∈(-1,1).  We find that the exchange-correlation energy tends to be minimized when ν_f is close to zero for as many flavors as possible, explaining the cascade flavor-symmetry-breaking pattern identified experimentally, and that the correlation energy favors metallic states over insulating states.