One-dimensional Luttinger liquids in a two-dimensional moiré lattice

The Luttinger liquid (LL) model of one-dimensional (1D) electronic systems provides a powerful tool for understanding strongly correlated physics, including phenomena such as spin–charge separation. Substantial theoretical efforts have attempted to extend the LL phenomenology to two dimensions, especially in models of closely packed arrays of 1D quantum wires, each being described as a LL. Such coupled-wire models have been successfully used to construct two-dimensional (2D) anisotropic non-Fermi liquids, quantum Hall states, topological phases and quantum spin liquids. However, an experimental demonstration of high-quality arrays of 1D LLs suitable for realizing these models remains absent. Here we report the experimental realization of 2D arrays of 1D LLs with crystalline quality in a moiré superlattice made of twisted bilayer tungsten ditelluride (tWTe2). Originating from the anisotropic lattice of the monolayer, the moiré pattern of tWTe2 hosts identical, parallel 1D electronic channels, separated by a fixed nanoscale distance, which is tuneable by the interlayer twist angle. At a twist angle of approximately 5 degrees, we find that hole-doped tWTe2 exhibits exceptionally large transport anisotropy with a resistance ratio of around 1,000 between two orthogonal in-plane directions. The across-wire conductance exhibits power-law scaling behaviours, consistent with the formation of a 2D anisotropic phase that resembles an array of LLs. Our results open the door for realizing a variety of correlated and topological quantum phases based on coupled-wire models and LL physics

Strong disorder RG approach – a short review of recent developments

The strong disorder RG approach for random systems has been extended in many new directions since our previous review of 2005 [F. Igloi, C. Monthus, Phys. Rep. 412, 277 (2005)]. The aim of the present colloquium paper is thus to give an overview of these various recent developments. In the field of quantum disordered models, recent progress concern infinite disorder fixed points for short-ranged models in higher dimensions d > 1, strong disorder fixed points for long-ranged models, scaling of the entanglement entropy in critical ground-states and after quantum quenches, the RSRG-X procedure to construct the whole set excited stated and the RSRG-t procedure for the unitary dynamics in many-body-localized phases, the Floquet dynamics of periodically driven chains, the dissipative effects induced by the coupling to external baths, and Anderson Localization models. In the field of classical disordered models, new applications include the contact process for epidemic spreading, the strong disorder renormalization procedure for general master equations, the localization properties of random elastic networks, and the synchronization of interacting non-linear dissipative oscillators. Application of the method for aperiodic (or deterministic) disorder is also mentioned