Evidence for Two Dimensional Anisotropic Luttinger Liquids at Millikelvin Temperatures

While Landau's Fermi liquid theory provides the standard description for two- and three-dimensional (2D/3D) conductors, the physics of interacting one-dimensional (1D) conductors is governed by the distinct Luttinger liquid (LL) theory. Can a LL-like state, in which electronic excitations are fractionalized modes, emerge in a 2D system as a stable zero-temperature phase? This long-standing question, first brought up by Anderson decades ago, is crucial in the study of non-Fermi liquids but remains unsettled. A recent experiment identified a moir\'e superlattice of twisted bilayer tungsten ditelluride (tWTe_2) with a small interlayer twist angle as a 2D host of the LL physics at temperatures of a few kelvins. Here we report experimental evidence for a 2D anisotropic LL state in a substantially reduced temperature regime, down to at least 50 mK, spontaneously formed in a tWTe_2 system with a twist angle of ~ 3 degree. While the system is metallic-like and nearly isotropic above 2 K, a dramatically enhanced electronic anisotropy develops in the millikelvin regime, featuring distinct transport behaviors along two orthogonal in-plane directions. In the strongly anisotropic phase, we observe transport characteristics of a 2D LL phase, i.e., the universal power law scaling behaviors in across-wire conductance and a zero-bias dip in the differential resistance along the wire direction. Our results represent a step forward in the search for stable LL physics beyond 1D and related unconventional quantum matter.