Tomonaga-Luttinger Liquid in a Box: Electrons Confined within MoS2 Mirror-Twin Boundaries

Abstract

Two-or three-dimensional metals are usually well described by weakly interacting, fermionic quasiparticles. This concept breaks down in one dimension due to strong Coulomb interactions. There, low-energy electronic excitations are expected to be bosonic collective modes, which fractionalize into independent spin and charge density waves. Experimental research on one-dimensional metals is still hampered by their difficult realization, their limited accessibility to measurements, and by competing or obscuring effects such as Peierls distortions or zero bias anomalies. Here we overcome these difficulties by constructing a well-isolated, one-dimensional metal of finite length present in MoS2 mirror twin boundaries. Using scanning tunneling spectroscopy we measure the single-particle density of the interacting electron system as a function of energy and position in the 1D box. Comparison to theoretical modeling provides unambiguous evidence that we are observing spin-charge separation in real space.

Possible Luttinger liquid behavior of edge transport in monolayer transition metal dichalcogenide crystals

“…We have witnessed two previous works demonstrate that the metallic mirror-twin boundaries in MoS 2 33 and MoSe 2 34 show Luttinger liquid behavior, in which the Luttinger parameter g are extracted to be 0.2 for MoS 2 33 and 0.5 for MoSe 2 34 , respectively. These values are much larger than the parameter g (0.11-0.08) extracted in our experiment from edge states, indicating that stronger electron-electron (or hole-hole) repulsive interactions along the edges of TMD than the one at the grain boundaries of TMD.…”

Band Bending and Valence Band Quantization at Line Defects in MoS2

“…They are derived from the 1D metallic MTB bands in the band gap of the 2D MoS 2 . 22 Their quantization and Coulomb-blockade energy gap, associated with the Tomonaga-Luttinger liquid hosted along the finite-length MTB, 22 are visible close to E F .…”

“…Charge transfer from Gr into in-gap defect bands is of decisive importance for band bending and the formation of the hole confining potential in the VB, meaning that this effect is substrate-tunable. [22][23][24][25] In MoSe 2 and MoTe 2 the 4|4P-type MTB is energetically most favorable, while in MoS 2 both 4|4P-and 4|4E-types are stable. 21,26 In our samples, 4|4E-type MTBs are about 5 times more common and typically longer than 4|4P-type.…”

Direct Observation of One-Dimensional Peierls-type Charge Density Wave in Twin Boundaries of Monolayer MoTe2

“…Recently, the conductive MTB embedded inside monolayer TMDC has been recognized as a newly discovered 1D metallic system. 7 The underlying mechanism of the charge modulation and electronic properties of different 1D MTBs are controversial, [8][9][10][11][12] even with similar experimental phenomena, such as electron density modulation with a 3a period in a so-called 4|4P MTB 9,10,12 and 2a period in so-called 4|4E MTB, 11 suppression of the density of states (DOS) near the Fermi energy (EF) at low temperature, and enhanced peaks cross EF. Barja et al 10 attributed the charge density modulation in MoSe2/bilayer graphene/SiC(0001) and an energy gap to the formation of CDW by theoretically considering lattice distortion.…”

“…Liu et al 9 argued that the interaction between MoSe2 and highly ordered pyrolytic graphite substrate forms a quantum well barrier, which induces different periodicity of electron density modulation at corresponding mapping energies. By focusing on 4|4E MTB and taking proper electron-electron interaction into account, Jolie et al 11 rule out the CDW state in MoS2/graphene/Ir(111) system, but report a Tomonaga-Luttinger liquid (TLL) ground state with charge-spin separation, according to the observed non-equidistant quantized satellite peaks and unusual spatial distributions along with the MTB. Most recently, on 4|4P MTB in the MoSe2/graphene system, 12 a signal of TLL state was claimed to be present.…”