A microscopic continuum model for symmetry-mismatched moiré interfaces shows that a rectangular substrate can fold the valleys of a honeycomb monolayer into quasi-one-dimensional wires with Sliding Luttinger Liquid physics, and can also realize topological flat bands.
Twisted coupled wire model for a moir\'e sliding Luttinger liquid
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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.
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Sliding Luttinger Liquid and Topological Flat Bands in Symmetry Mismatched Moir\'e Interfaces
A microscopic continuum model for symmetry-mismatched moiré interfaces shows that a rectangular substrate can fold the valleys of a honeycomb monolayer into quasi-one-dimensional wires with Sliding Luttinger Liquid physics, and can also realize topological flat bands.