  One-dimensional (1D) interacting electrons are often described as a Luttinger
liquid1-4 having properties that are intrinsically different from Fermi liquids
in higher dimensions5,6. 1D electrons in materials systems exhibit exotic
quantum phenomena that can be tuned by both intra- and inter-1D-chain
electronic interactions, but their experimental characterization can be
challenging. Here we demonstrate 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 have imaged the evolution of DW
Luttinger liquids under different interaction regimes tuned by electron density
using a novel scanning tunneling microscopy (STM) technique. Single DWs at low
carrier density are highly susceptible to Wigner crystallization consistent
with a spin-incoherent Luttinger liquid, while at intermediate densities
dimerized Wigner crystals form due to an enhanced magneto-elastic coupling.
Periodic arrays of DWs exhibit an interplay between intra- and inter-chain
interactions that gives rise to new quantum phases. At low electron densities
inter-chain interactions are dominant and induce a 2D electron crystal composed
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 where electrons are ordered with
algebraical correlation decay along the chain direction but disordered between
chains. Our work shows that layer-stacking DWs in 2D heterostructures offers
new opportunities to explore Luttinger liquid physics.
