Correlated States Of A Triangular Net Of Coupled Quantum Wires: Implications For The Phase Diagram Of Marginally Twisted Bilayer Graphene

We explore in detail the electronic phases of a system consisting of three noncolinear 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 s-wave 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 in magic-angle twisted samples, as well as the "strange metal" behavior at finite temperatures as a natural outcome of the 2D Luttinger liquid phase.