Optical and electronic phenomena in solids arise from the behaviour of electrons and holes (unoccupied states in a filled electron sea). Electron–hole symmetry can often be invoked as a simplifying description, which states that electrons with energy above the Fermi sea behave the same as holes below the Fermi energy. In semiconductors, however, electron–hole symmetry is generally absent, because the energy-band structure of the conduction band differs from the valence band1. Here we report on measurements of the discrete, quantized-energy spectrum of electrons and holes in a semiconducting carbon nanotube2. By applying a voltage to a gate electrode, an individual nanotube is filled controllably with a precise number of either electrons or holes, starting from one. The discrete excitation spectrum for a nanotube with N holes is strikingly similar to the corresponding spectrum for N electrons. This observation of near-perfect electron–hole symmetry3 demonstrates that a semiconducting nanotube can be free of charged impurities, even in the limit of few electrons or holes. We furthermore find an anomalously small Zeeman spin splitting and an excitation spectrum indicating strong electron–electron interactions.
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We thank R. E. Smalley and co-workers for providing the high-quality HiPco nanotubes, and S. De Franceschi, J. Kong, K. Williams, Y. Nazarov, H. Postma, S. Lemay and J. Fernández-Rossier for discussions. We acknowledge the technical assistance of R. Schouten, B. van der Enden and M. van Oossanen. Financial support was obtained from the Dutch Organization for Fundamental Research (FOM).
The authors declare that they have no competing financial interests.
FigS1 shows a scheme of the band diagram. FigS2 shows additional data from a different semiconducting nanotube. FigS3 shows Zeeman splitting in a magnetic field. (PDF 1585 kb)
Supplementary discussion/legends related to the supplementary figures; 1) Model calculations; 2) Scattering and disorder; 3) Zeeman splitting. (DOC 29 kb)
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Jarillo-Herrero, P., Sapmaz, S., Dekker, C. et al. Electron-hole symmetry in a semiconducting carbon nanotube quantum dot. Nature 429, 389–392 (2004). https://doi.org/10.1038/nature02568
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