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One-dimensional electron systems (1DESs) exhibit properties that arefundamentally different from higher-dimensional systems. For example,electron-electron interactions in 1DESs have been predicted to induceTomonaga-Luttinger liquid behavior. Naturally-occurring grain boundaries insingle-layer semiconducting transition metal dichalcogenides provide 1Dconducting channels that have been proposed to host Tomonaga-Luttinger liquids,but charge density wave physics has also been suggested to explain theirbehavior. Clear identification of the electronic ground state of this systemhas been hampered by an inability to electrostatically gate such boundaries andthereby tune their charge carrier concentration. Here we present a scanningtunneling microscopy/spectroscopy study of gate-tunable mirror twin boundaries(MTBs) in single-layer 1H-MoSe$_2$ devices. Gating here enables STMspectroscopy to be performed for different MTB electron densities, thusallowing precise characterization of electron-electron interaction effects.Visualization of MTB electronic structure under these conditions allowsunambiguous identification of collective density wave excitations having twodistinct velocities, in quantitative agreement with the spin-charge separationpredicted by finite-length Tomonaga-Luttinger-liquid theory.

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