We explore in detail the electronic phases of a system consisting of three noncolinear arrays of coupled quantum wires, each rotated ${120}^{\circ }$ with respect to the next. A perturbative renormalization-group analysis reveals that multiple correlated states can be stabilized: a $s$-wave or $d\pm id$ 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.

• Received 6 August 2019
• Revised 6 February 2020
• Accepted 6 April 2020

DOI:https://doi.org/10.1103/PhysRevB.101.165431