Twisted coupled wire model for a moiré sliding Luttinger liquid

Recent experiments in twisted bilayer WTe${}_2$ revealed the existence of anisotropic Luttinger liquid behavior. To generically characterize such anisotropic twisted bilayer systems, we study a model of a twisted bilayer of two-dimensional (2D) arrays of coupled wires, which effectively form an array of coupled moiré wires. We solve the model by the transfer matrix method, and identify quasi-1D electron bands in the system at small twist angles. With electron interactions added, we show that the moiré wires have an effective Luttinger parameter $g_{\text{eff}}$ much lower than that of the microscopic wires. This leads to a sliding Luttinger liquid (SLL) temperature regime, in which power-law current voltage relations arise. For parameters partly estimated from WTe${}_2$, a microscopic interaction $U\sim 0.7$eV yields a temperature regime of SLL similar to that in the WTe${}_2$ experiments.