Correlation of Electron Tunneling and Plasmon Propagation in a Luttinger Liquid

Zhao, Sihan; Wang, Sheng; Wu, Fanqi; Shi, Wu; Utama, M. Iqbal Bakti; Lyu, Tairu; Jiang, Lili; Su, Yudan; Wang, Siqi; Watanabe, Kenji; Taniguchi, Takashi; Zettl, Alex; Zhang, Xiang; Zhou, Chongwu; Wang, Feng

doi:10.1103/physrevlett.121.047702

Cited by 24 publications

(19 citation statements)

References 31 publications

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“…The parameters from all MoS 2 and WSe 2 devices are summarized in the Supplementary Table 1 in Supplemental Information. All these data here demonstrates that the Luttinger parameter g ≪ 1, as often discussed in Luttinger model 24,27,30,31 , indicating a strong repulsive electron-electron (hole-hole) interactions along 1D charge transport path in edgestate-dominated MoS 2 (WSe 2 ) crystals and this result can be generally extended to all semiconducting TMD crystals.…”

Section: Resultssupporting

confidence: 70%

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

et al. 2020

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In atomically-thin two-dimensional (2D) semiconductors, the nonuniformity in current flow due to its edge states may alter and even dictate the charge transport properties of the entire device. However, the influence of the edge states on electrical transport in 2D materials has not been sufficiently explored to date. Here, we systematically quantify the edge state contribution to electrical transport in monolayer MoS 2 /WSe 2 field-effect transistors, revealing that the charge transport at low temperature is dominated by the edge conduction with the nonlinear behavior. The metallic edge states are revealed by scanning probe microscopy, scanning Kelvin probe force microscopy and first-principle calculations. Further analyses demonstrate that the edge-state dominated nonlinear transport shows a universal power-law scaling relationship with both temperature and bias voltage, which can be well explained by the 1D Luttinger liquid theory. These findings demonstrate the Luttinger liquid behavior in 2D materials and offer important insights into designing 2D electronics.

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Section: Resultssupporting

confidence: 70%

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

et al. 2020

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“…Ultraclean SWNTs were directly grown on exfoliated hexagonal boron nitride (h-BN) flakes on silicon substrate with 285 nm oxide layers by chemical vapor deposition (CVD) 25,29 . Different species of SWNTs on h-BN substrates can be grown by such CVD processes.…”

Section: Resultsmentioning

confidence: 99%

“…Near-field line profiles along the nanotubes represented by the solid lines in Figure 2a reveal how the plasmon wave gets damped as it propagates. For a quantitative study, we can extract both the plasmon wavelength λ P and quality factor Q as a function of diameter by fitting the line profiles with a damped oscillator form e −2πx (Q⋅λ P ) ⁄ sin�(4πx) λ p ⁄ � from the nanotube end 24,25 . The fitting curves for each diameter are shown in dashed lines in Figure 2a.…”

Section: Resultsmentioning

confidence: 99%

Logarithm Diameter Scaling and Carrier Density Independence of One-Dimensional Luttinger Liquid Plasmon

Wang

Zhao

et al. 2019

Nano Lett.

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Quantum-confined electrons in one-dimensional (1D) metals are described by a Luttinger liquid. The collective charge excitations (i.e. plasmons) in a Luttinger liquid can behave qualitatively different from their conventional counterparts. For example, the Luttinger liquid plasmon velocity is uniquely determined by the electron-electron interaction, which scales logarithmly with the diameter of the 1D material. In addition, the Luttinger liquid plasmon is predicted to be independent on the carrier concentration. Here, we report the observation of such unusual Luttinger liquid plasmon behaviors in metallic single walled carbon nanotubes, a model system featuring strong electron quantum confinement. We systematically investigate the plasmon propagation in over 30 metallic carbon nanotubes of different diameters using infrared nanoscopy. We establish that the plasmon velocity has a weak logarithm dependence on the nanotube diameter, as predicted by the Luttinger liquid theory. We further study the plasmon excitation as a function of the carrier density in electrostatically gated metallic carbon nanotubes, and demonstrate that the plasmon velocity is completely independent on the carrier density. These behaviors are in striking contrast to conventional plasmons in 1D metallic shells, where the plasmon dispersion changes dramatically with the metal electron density and the 1D diameter. The unusual behaviors of Luttinger liquid plasmon may enable novel nanophotonic applications based on carbon nanotubes.

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“…2) for all electronic systems in different dimensions is derived, which could capture the most fundamental features of plasmons. Importantly, a universal mechanism for realizing a DIP is devised, shedding important insights in understanding the DIPs excited in the 2D nodal line systems as well as 3D nodal-surface (28) and 1D nodal-point (27,44,48) systems. Second, new terahertz metamaterials based on a large number of TSMs are designed to achieve a terahertz-stable spectroscopy from narrowband to broadband or a quantized manipulation of terahertz frequencies.…”

Section: Discussionmentioning

confidence: 99%

Density-independent plasmons for terahertz-stable topological metamaterials

Wang

Sui

Duan

et al. 2021

Proc. Natl. Acad. Sci. U.S.A.

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To efficiently integrate cutting-edge terahertz technology into compact devices, the highly confined terahertz plasmons are attracting intensive attention. Compared to plasmons at visible frequencies in metals, terahertz plasmons, typically in lightly doped semiconductors or graphene, are sensitive to carrier density (n) and thus have an easy tunability, which leads to unstable or imprecise terahertz spectra. By deriving a simplified but universal form of plasmon frequencies, here, we reveal a unified mechanism for generating unusual n-independent plasmons (DIPs) in all topological states with different dimensions. Remarkably, we predict that terahertz DIPs can be excited in a two-dimensional nodal line and one-dimensional nodal point systems, confirmed by the first-principle calculations on almost all existing topological semimetals with diverse lattice symmetries. Besides n-independence, the feature of Fermi velocity and degeneracy factor dependencies in DIPs can be applied to design topological superlattice and multiwalled carbon nanotube metamaterials for broadband terahertz spectroscopy and quantized terahertz plasmons, respectively. Surprisingly, high spatial confinement and quality factor, also insensitive to n, can be simultaneously achieved in these terahertz DIPs. Our findings pave the way for developing topological plasmonic devices for stable terahertz applications.

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Correlation of Electron Tunneling and Plasmon Propagation in a Luttinger Liquid

Cited by 24 publications

References 31 publications

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

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

Logarithm Diameter Scaling and Carrier Density Independence of One-Dimensional Luttinger Liquid Plasmon

Density-independent plasmons for terahertz-stable topological metamaterials

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