Recent experiments in twisted bilayer ${\mathrm{WTe}}_2$ 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 $g_{\text{eff}}$ 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 ${\mathrm{WTe}}_2$, a microscopic interaction $U\sim 3\mathrm{eV}$ yields a temperature regime of SLL similar to that in the ${\mathrm{WTe}}_2$ experiments.

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• Quantum transport
• 2-dimensional systems
• Nanostructures
• Transition metal dichalcogenides
• Luttinger liquid model
• Transfer matrix calculations