Correlated states of a triangular net of coupled quantum wires: Implications for the phase diagram of marginally twisted bilayer graphene
Chuan Chen, A. H. Castro Neto, Vitor M. Pereira
Abstract
We explore in detail the electronic phases of a system consisting of three noncolinear arrays of coupled quantum wires, each rotated ${120}^{\ensuremath{\circ}}$ with respect to the next. A perturbative renormalization-group analysis reveals that multiple correlated states can be stabilized: a $s$-wave or $d\phantom{\rule{0.16em}{0ex}}\ifmmode\pm\else\textpm\fi{}\phantom{\rule{0.16em}{0ex}}id$ 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.