On the electronic phases of magically twisted bilayer graphene

We explore in detail the electronic phases of a system consisting of three non-colinear arrays of coupled quantum wires, each rotated 120 degrees with respect to the next. A perturbative renormalization-group analysis reveals that multiple correlated states can be stabilized: a smectic or d ± id superconductor, a charge density wave insulator, a two-dimensional Fermi liquid, and a 2D Luttinger liquid (also known as smectic metal or sliding Luttinger liquid). The model provides an effective description of electronic interactions in small-angle twisted bilayer graphene and we discuss its implications in relation to the recent observation of correlated and superconducting ground states near commensurate densities, as well as the “strange metal” behaviour at finite temperatures as a natural outcome of the 2D Luttinger liquid phase.