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Observation and spectroscopy of a two-electron Wigner molecule in an ultraclean carbon nanotube

Nature Physics volume 9, pages 576–581 (2013)Cite this article

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Abstract

Two electrons on a string form a simple model system where Coulomb interactions are expected to play an interesting role. In the presence of strong interactions, these electrons are predicted to form a Wigner molecule, separating to the ends of the string. This spatial structure is believed to be clearly imprinted on the energy spectrum, yet so far a direct measurement of such a spectrum in a controllable one-dimensional setting is still missing. Here we use an ultraclean carbon nanotube to realize this system in a tunable potential. Using tunnelling spectroscopy we measure the addition spectra of two interacting carriers, electrons or holes, and identify seven low-energy states characterized by their exchange symmetries. The formation of a Wigner molecule is evident from a tenfold quenching of the fundamental excitation energy as compared with the non-interacting value. Our ability to tune the two-carrier state in space and to study it for both electrons and holes provides an unambiguous demonstration of this strongly interacting quantum ground state.

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Figure 1: Addition energy spectra of a two-electron molecular state in an ultraclean nanotube.
Figure 2: Addition energy spectra predicted for two non-interacting and two strongly interacting electrons in a nanotube.
Figure 3: Magnetic-dependent spectra of the two-electron molecular states at different detunings.
Figure 4: Quenching of excitation energies in a Wigner molecule.

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Acknowledgements

We would like to acknowledge E. Berg, A. Stern, A. Yacoby and B. Wunsch for useful discussions. S.I. acknowledges the financial support by the ISF Legacy Heritage foundation (2005/08-80.0), the Bi-National science foundation (BSF 710647-03), the Minerva foundation, the ERC starters grant (258753), the Marie Curie People grant (IRG 239322), and the Alon fellowship. S.I. is incumbent of the William Z. and Eda Bess Novick career development chair. P.L.M. and D.C.R. acknowledge support by the NSF through the Center for Nanoscale systems (EEC-0646547), by the NSF through DMR-1010768, and by the MARCO Focused Research Center on Materials, Structures and Devices. The experiments used the facilities of the Cornell node of the National Nanotechnology Infrastructure Network (EECS-0335765) and the Cornell Center for Materials Research (DMR-1120296), both funded by NSF. M.R. and A.S. acknowledge support from Fondazione Cassa di Risparmio di Modena through the project COLD and FEW, from EU through the Marie Curie ITN INDEX, and from the CINECA-ISCRA supercomputing grant IscrC_TUN1DFEW. F.K. acknowledges support by the Center for Quantum Devices, funded by the Danish National Research Foundation.

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Author notes

  1. A. Secchi

    Present address: Present address: Institute for Molecules and Materials, Radboud University of Nijmegen, 6525 AJ Nijmegen, The Netherlands,

  2. S. Pecker and F. Kuemmeth: These authors contributed equally to this work

Authors and Affiliations

  1. Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel

    S. Pecker & S. Ilani

  2. Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen, Denmark

    F. Kuemmeth

  3. CNR–NANO Research Center S3, Via Campi 213/a, 41125 Modena, Italy

    A. Secchi & M. Rontani

  4. Department of Physics, University of Modena and Reggio Emilia, 41125 Modena, Italy

    A. Secchi

  5. Physics Department, Cornell University, Ithaca, New York 14853, USA

    D. C. Ralph & P. L. McEuen

  6. Kavli Institute at Cornell, Cornell University, Ithaca, New York 14853, USA

    D. C. Ralph & P. L. McEuen

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Contributions

F.K., S.I., D.C.R. and P.L.M. conceived and designed the experiments. F.K. and S.I. performed the experiments. S.P., A.S. and M.R. provided theoretical tools for analysing the data. S.P., F.K., A.S., M.R. and S.I. analysed the data. S.P. and S.I. wrote the manuscript and all authors contributed to its final version.

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Correspondence to S. Ilani.

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The authors declare no competing financial interests.

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Pecker, S., Kuemmeth, F., Secchi, A. et al. Observation and spectroscopy of a two-electron Wigner molecule in an ultraclean carbon nanotube. Nature Phys 9, 576–581 (2013). https://doi.org/10.1038/nphys2692

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