Twisted coupled wire model for a moir\'e sliding Luttinger liquid

TL;DR

This paper models twisted bilayer WTe2 as an array of coupled moiré wires, revealing a sliding Luttinger liquid regime with distinct power-law behaviors, consistent with experimental observations.

Contribution

It introduces a twisted coupled wire model to describe anisotropic moiré systems and demonstrates the emergence of a sliding Luttinger liquid regime with realistic parameters.

Findings

Identification of quasi-1D electron bands at small twist angles.

Effective Luttinger parameter $g_{eff}$ is significantly lower than microscopic wires.

Prediction of a temperature regime exhibiting power-law current-voltage relations.

Abstract

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 moir\'e 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 moir\'e 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 $U\sim0.7$eV yields a temperature regime of SLL similar to that in the WTe$_2$ experiments.