Tunable Luttinger liquid and correlated insulating states in one-dimensional moiré superlattices

Two-dimensional moiré superlattices have been extensively studied, and a variety of correlated phenomena have been observed. However, their lower-dimensional counterpart, one-dimensional (1D) moiré superlattices, remain largely unexplored. Electrons in 1D are generally described by Luttinger liquid theory, with universal scaling relations depending only on the Luttinger parameter g. In particular, at half-filling, Umklapp scattering plays a crucial role, as it can significantly change the conductance-temperature scaling relation and lead to Mott insulators. However, this prediction has never been observed since doping an empty band to half-filling was extremely difficult. Here, we show that the marriage of moiré superlattices and 1D electrons makes it possible to study the Luttinger liquid in an exceptionally wide filling region simply by electrical gating. We perform transport measurements on 1D moiré superlattices of carbon nanotubes on hexagonal boron nitride (hBN) substrates, and observe correlated insulating states at 1/4 and 1/2 fillings of the superlattice mini-band, where Umklapp scattering becomes dominant. We also observe a T-linear conductance at these commensurate fillings over a range of temperatures. Strikingly, the T-linear conductance leads to a strongly suppressed Luttinger parameter, suggesting a state of extreme correlation.