  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.
