Interacting electrons in one dimension are often described as Luttinger liquids, having properties intrinsically different from Fermi liquids in higher dimensions. Luttinger liquids exhibit exotic quantum phenomena such as scale-invariant correlation tunable by interaction strength, but their experimental characterization can be challenging. Our work [1] demonstrates that layer-stacking domain walls (DWs) in van der Waals heterostructures form a broadly tunable Luttinger liquid system, including both isolated and coupled arrays. We use scanning tunneling microscopy to image the evolution of DW Luttinger liquids under different interaction regimes. Single DWs at low carrier density are highly susceptible to Wigner crystallization, whereas at intermediate densities dimerized Wigner crystals form because of an enhanced magneto-elastic coupling. Periodic arrays of DWs exhibit an interplay between intra- and inter-chain interactions giving rise to new quantum phases: At low electron densities, dominant inter-chain interactions induce a 2D electron crystal of phased-locked 1D Wigner crystal in a staggered configuration; Increased electron density causes intra-chain fluctuation potentials to dominate, leading to an electronic smectic liquid crystal phase with algebraical correlation decay along the chain direction but disordered between chains. Our work shows that layer-stacking DWs in 2D heterostructures provide opportunities to explore Luttinger liquid physics.
[1] H. Li et. al, Nature 631, 765–770 (2024)