Tomonaga-Luttinger liquid and charge-density wave in a quasi-one-dimensional material

TL;DR

This study reports the discovery of a quasi-one-dimensional material, Cs$_{1- ext{delta}}$Cr$_3$S$_3$, that uniquely exhibits coexistence of charge-density wave and Tomonaga-Luttinger liquid states, enabling exploration of intertwined quantum phenomena.

Contribution

The paper presents the first observation of coexistence of CDW and TLL states in a real quasi-1D material, supported by experimental and theoretical evidence.

Findings

Cs$_{1- ext{delta}}$Cr$_3$S$_3$ exhibits both CDW and TLL states.

Optical measurements show a 250 meV band gap due to CDW.

Transport and ARPES confirm TLL behavior with power-law scaling.

Abstract

In one-dimensional (1D) electron systems, the Fermi liquid state breaks down due either to electron interactions, which results in a Tomonaga-Luttinger liquid (TLL) state, or to Peierls instability, which leads to an insulating charge-density-wave (CDW) phase. In general, these two phenomena are mutually exclusive, and their coexistence remains elusive in real materials. Here, we report the discovery of a new quasi-1D material, Cs$_{1-\delta}$Cr$_3$S$_3$, which unexpectedly exhibits coexistence of the antithetical CDW and TLL states. The CDW state is evidenced by the intra-unit-cell dimerization, and the opening of an optical band gap of $\sim$250 meV. Meanwhile, TLL behaviour is unambiguously demonstrated by the measurements of electrical transport and angle-resolved photoemission spectroscopy, which reveal a power-law scaling with temperature, bias voltage and electron energy. Band structure calculations reveal isolated, linearly dispersive, 1D bands around the Fermi level. For the dimerized CDW phase, the 1D Fermi-surface sheets located at the boundary of the Brillouin zone are gapped from intra-unit-cell bond symmetry breaking. Experimentally, subtle Cs vacancies shift the Fermi level into the linearly dispersive valence band, enabling the observation of TLL behaviour without interrupting the CDW order. This work establishes Cs$_{1-\delta}$Cr$_3$S$_3$ as a rare material platform in which the antagonistic Fermi-liquid instabilities coexist and intertwine, opening new avenues for studying emergent quantum phenomena in 1D systems.