Imaging gate-tunable Tomonaga-Luttinger liquids in 1H-MoSe$_2$ mirror twin boundaries

TL;DR

This study demonstrates gate-tunable mirror twin boundaries in 1H-MoSe2 as a platform for observing Tomonaga-Luttinger liquid behavior, providing direct evidence of spin-charge separation through STM spectroscopy.

Contribution

It introduces a method to electrostatically gate 1D boundaries in MoSe2, enabling direct spectroscopic observation of Tomonaga-Luttinger liquid phenomena.

Findings

Observation of two distinct velocities in density wave excitations.

Quantitative agreement with spin-charge separation predictions.

Confirmation of Tomonaga-Luttinger liquid behavior in 1H-MoSe2 boundaries.

Abstract

One-dimensional electron systems (1DESs) exhibit properties that are fundamentally different from higher-dimensional systems. For example, electron-electron interactions in 1DESs have been predicted to induce Tomonaga-Luttinger liquid behavior. Naturally-occurring grain boundaries in single-layer semiconducting transition metal dichalcogenides provide 1D conducting channels that have been proposed to host Tomonaga-Luttinger liquids, but charge density wave physics has also been suggested to explain their behavior. Clear identification of the electronic ground state of this system has been hampered by an inability to electrostatically gate such boundaries and thereby tune their charge carrier concentration. Here we present a scanning tunneling microscopy/spectroscopy study of gate-tunable mirror twin boundaries (MTBs) in single-layer 1H-MoSe$_2$ devices. Gating here enables STM spectroscopy to be performed for different MTB electron densities, thus allowing precise characterization of electron-electron interaction effects. Visualization of MTB electronic structure under these conditions allows unambiguous identification of collective density wave excitations having two distinct velocities, in quantitative agreement with the spin-charge separation predicted by finite-length Tomonaga-Luttinger-liquid theory.