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Nonlinear Luttinger liquid plasmons in semiconducting single-walled carbon nanotubes

Abstract

Interacting electrons confined in one dimension are generally described by the Luttinger liquid formalism, where the low-energy electronic dispersion is assumed to be linear and the resulting plasmonic excitations are non-interacting. Instead, a Luttinger liquid in one-dimensional materials with nonlinear electronic bands is expected to show strong plasmon–plasmon interactions, but an experimental demonstration of this behaviour has been lacking. Here, we combine infrared nano-imaging and electronic transport to investigate the behaviour of plasmonic excitations in semiconducting single-walled carbon nanotubes with carrier density controlled by electrostatic gating. We show that both the propagation velocity and the dynamic damping of plasmons can be tuned continuously, which is well captured by the nonlinear Luttinger liquid theory. These results contrast with the gate-independent plasmons observed in metallic nanotubes, as expected for a linear Luttinger liquid. Our findings provide an experimental demonstration of one-dimensional electron dynamics beyond the conventional linear Luttinger liquid paradigm and are important for understanding excited-state properties in one dimension.

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Fig. 1: Schematic of IR-SNOM of SWNTs with carrier density controlled by electrostatic gating.
Fig. 2: Infrared nano-imaging of metallic and semiconducting SWNTs at different gate voltages.
Fig. 3: Gate-tunable plasmons in semiconducting SWNTs.
Fig. 4: Nonlinear Luttinger liquid model and comparison with experimental results.

Data availability

The numerical data represented in Fig. 4b–d are provided with the paper as source data. All other data that support results in this Article are available from the corresponding author upon reasonable request.

Code availability

Matlab codes for nonlinear theory calculation are available from the corresponding author upon reasonable request.

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Acknowledgements

We thank N. Yao, R. Vasseur, J. Kang and H. B. Balch for helpful discussions. This work was mainly supported by the Director, Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering Division of the US Department of Energy under contract no. DE-AC02-05-CH11231 (sp2-Bonded Materials Program KC2207). The device fabrication and electrical measurement were supported by the Office of Naval Research (MURI award N00014-16-1-2921). The data analysis was supported by the NSF award 1808635. Z.S. acknowledges support from the National Natural Science Foundation of China (11774224 and 11574204). F. Wu, Z.Z. and C.Z. acknowledge the National Science Foundation for financial support under grant no. 769K521. K.W. and T.T. acknowledge support from the Elemental Strategy Initiative conducted by the MEXT, Japan and the CREST (JPMJCR15F3), JST.

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F. Wang, S.W. and Z.S. conceived the project and designed the experiment. F. Wang and C.Z. supervised the project. S.W. fabricated the devices and performed the infrared nano-imaging measurements. S.Z. and S.W. fabricated the devices for the transport measurements and carried out the electrical measurements. F. Wu and Z.Z. under the supervision of C.Z. grew the SWNT samples and performed scanning electron microscopy. Z.S., L.J. and A.Z. assisted in device fabrication. K.W. and T.T. provided the h-BN crystals. S.W. and F. Wang analysed the data. All authors contributed to the writing of the manuscript.

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Correspondence to Feng Wang.

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Supplementary Information

Supplementary Figs. 1–3, discussion

Source data

Source Data Fig. 4

Numerical data used to generate Fig. 4b–d

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Wang, S., Zhao, S., Shi, Z. et al. Nonlinear Luttinger liquid plasmons in semiconducting single-walled carbon nanotubes. Nat. Mater. 19, 986–991 (2020). https://doi.org/10.1038/s41563-020-0652-5

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