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The one-dimensional Wigner crystal in carbon nanotubes

Nature Physics volume 4, pages 314–318 (2008)Cite this article

Abstract

A dilute system of electrons interacting through long-range Coulomb forces has been predicted to form a periodic solid known as a Wigner crystal. To date, this state has been observed directly only in two-dimensional systems. Here, using low-temperature single-electron transport spectroscopy, we show that the hole gas in low-disorder semiconducting carbon nanotubes forms a one-dimensional Wigner crystal. In an axial magnetic field, we observe three distinct regimes of spin and isospin polarization as carrier density is varied. We explain these regimes in terms of a Wigner crystal picture based on a gapped Luttinger liquid model, with the carriers represented by spatially localized solitons. Our observations could enable greater control over the behaviour of the spatially separated system of carriers. Such control, combined with the inherently long coherence times of carriers in carbon nanotubes, could prove useful in the development of solid-state quantum computing.

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Figure 1: Experimental geometry and characteristic transport data.
Figure 2: Transport spectroscopy and magnetic-field evolution of Coulomb peaks.
Figure 3: Energy shift of Coulomb peaks with B and schematic diagram of solitons corresponding to the four combination of spin and isospin.
Figure 4: Kondo effect and flavour configurations.

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Acknowledgements

We acknowledge Micro Nano Laboratory at Caltech and Nanotech at UCSB, where fabrication was carried out. We thank C. N. Lau, G. Fiete, G. Refael, R. Barnett, D. Novikov, P. Jarillo-Herrero, C. Marcus, B. Muralidharan and H. Van der Zant for discussions. We acknowledge the support of the Office of Naval Research and the Sloan foundation. We thank an anonymous referee for raising the question concerning the observability of the Kondo effect in our system.

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  1. Applied Physics, California Institute of Technology, Mail Stop 128-95, Pasadena, California 91125, USA

    Vikram V. Deshpande & Marc Bockrath

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  1. Vikram V. Deshpande
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Correspondence to Marc Bockrath.

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Supplementary Discussion and Supplementary Figure 1–3 (PDF 393 kb)

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Deshpande, V., Bockrath, M. The one-dimensional Wigner crystal in carbon nanotubes. Nature Phys 4, 314–318 (2008). https://doi.org/10.1038/nphys895

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