Tunable Luttinger Liquid Systems in van der Waals Heterostructures­

One-dimensional (1D) interacting electrons, known as the Luttinger liquid, are intrinsically different from the Fermi liquid at higher dimensions. They exhibit exotic quantum phenomena tuned by both the intra- and inter-1D-chain electronic interactions, while their experimental observations are challenging. Here we demonstrate the layer stacking domain walls (DWs) in van der Waals heterostructures as broadly tunable Luttinger liquid systems, including both isolated form and coupled arrays. Using a novel scanning tunneling microscopy technique, we imaged the evolution of the Luttinger liquid systems under various interaction regimes tuned by electron densities. In a single DW, we observed 1D Wigner crystals in the spin-incoherent Luttinger liquid regime at low electron densities, a dimerized Wigner crystal driven by the magneto-elastic coupling at intermediate electron densities, and a weakly interacting Luttinger liquid at high electron densities featuring the Freidel oscillation. In a periodic array of DWs, the interplay between the inter- and inter-chain interactions gives rise to new quantum phases. At low electron densities, the prominent inter-chain interaction induces a 2D electron crystal composed of phased-locked 1D Wigner crystal in a staggered configuration. At increased electron density, the intra-chain interactions dominate, leading to an electronic smectic liquid crystal phase where the electrons are ordered along the DW direction but disordered in the orthogonal direction. Our work shows that layer stacking DWs in 2D heterostructures offers tremendous opportunities to explore the Luttinger liquid physics.