Abstract
Quantum mechanical experiments in ring geometries have long fascinated physicists. Open rings connected to leads, for example, allow the observation of the Aharonov–Bohm effect1, one of the best examples of quantum mechanical phase coherence2,3. The phase coherence of electrons travelling through a quantum dot embedded in one arm of an open ring has also been demonstrated4. The energy spectra of closed rings5 have only recently been studied by optical spectroscopy6,7. The prediction that they allow persistent current8 has been explored in various experiments9,10,11. Here we report magnetotransport experiments on closed rings in the Coulomb blockade regime12. Our experiments show that a microscopic understanding of energy levels, so far limited to few-electron quantum dots13, can be extended to a many-electron system. A semiclassical interpretation of our results indicates that electron motion in the rings is governed by regular rather than chaotic motion, an unexplored regime in many-electron quantum dots. This opens a way to experiments where even more complex structures can be investigated at a quantum mechanical level.
This is a preview of subscription content, access via your institution
Access options
Subscribe to this journal
Receive 51 print issues and online access
$199.00 per year
only $3.90 per issue
Buy this article
- Purchase on Springer Link
- Instant access to full article PDF
Prices may be subject to local taxes which are calculated during checkout
Similar content being viewed by others
References
Aharonov, Y. & Bohm, D. Significance of electromagnetic potentials in the quantum theory. Phys. Rev. 115, 485–491 (1959).
Webb, R. A., Washburn, S., Umbach, C. P. & Laibowitz, R. B. Observation of h/e Aharonov-Bohm oscillations in normal-metal rings. Phys. Rev. Lett. 54, 2696–2699 (1985).
Timp, G. et al. Observation of the Aharonov-Bohm effect for ωcτ > 1. Phys. Rev. Lett. 58, 2814–2817 (1987).
Schuster, R. et al. Phase measurement in a quantum dot via a double-slit interference experiment. Nature 385, 417–420 (1997).
Byers, N. & Yang, C. N. Theoretical considerations concerning quantized magnetic flux in superconducting cylinders. Phys. Rev. Lett. 7, 46–49 (1961).
Lorke, A. et al. Spectroscopy of nanoscopic semiconductor rings. Phys. Rev. Lett. 84, 2223–2226 (2000).
Warburton, R. J. et al. Optical emission from a charge-tunable quantum ring. Nature 405, 926–929 (2000).
Büttiker, M., Imry, Y. & Landauer, R. Josephson behavior in small normal one-dimensional rings. Phys. Lett. A 96, 365–367 (1983).
Lévy, L. P., Dolan, G., Dunsmuir, J. & Bouchiat, H. Magnetization of mesoscopic copper rings: Evidence for persistent currents. Phys. Rev. Lett. 64, 2074–2077 (1990).
Chandrasekhar, V. et al. Magnetic response of a single, isolated gold loop. Phys. Rev. Lett. 67, 3578–3581 (1991).
Mailly, D., Chapelier, C. & Benoit, A. Experimental observation of persistent currents in GaAs-AlGaAs single loop. Phys. Rev. Lett. 70, 2020–2023 (1993).
Kouwenhoven, L. P. et al. in Nato ASI Conf. Proc. (eds Kouwenhoven, L. P., Schön, G. & Sohn, L. L.) 105–214 (Kluwer, Dordrecht, 1997).
Tarucha, S., Austing, D. G., Honda, T., van der Haage, R. J. & Kouwenhoven, L. P. Shell filling and spin effects in a few electron quantum dot. Phys. Rev. Lett. 77, 3613–3616 (1996).
Held, R. et al. In-plane gates and nanostructures fabricated by direct oxidation of semiconductor heterostructures with an atomic force microscope. Appl. Phys. Lett. 73, 262–264 (1998).
Lüscher, S., Heinzel, T., Ensslin, K., Wegscheider, W. & Bichler, M. Signatures of spin pairing in a quantum dot in the Coulomb blockade regime. Phys. Rev. Lett. 86, 2118–2121 (2001).
Heinzel, T. et al. Electronic properties of semiconductor nanostructures patterned by AFM lithography. Physica E 9, 84–93 (2001).
Pedersen, S., Hansen, A. E., Kristensen, A., Sorensen, S. B. & Lindelof, P:. E. Observation of quantum asymmetry in an Aharonov-Bohm ring. Phys. Rev. B 61, 5457–5460 (2000).
Cassé, M. et al. Temperature dependence of the Aharonov-Bohm oscillations and the energy spectrum in a single-mode ballistic ring. Phys. Rev. B 62, 2624–2629 (2000).
Tan, W.-C. & Inkson, J. C. Electron states in a two-dimensional ring—an exactly soluble model. Semicond. Sci. Technol. 11, 1635–1641 (1996).
Chakraborty, T. & Pietiläinen, P. Persistent currents in a quantum ring: Effects of impurities and interactions. Phys. Rev. B 52, 1932–1935 (1995).
Kastner, M. A. The single-electron transistor. Rev. Mod. Phys. 64, 849–858 (1992).
Berman, D., Entin-Wohlman, O. & Azbel, M. Y. Diamagnetic spectrum and oscillations in an elliptic shell. Phys. Rev. B 42, 9299–9306 (1990).
Beenakker, C. W. J. Random-matrix theory of quantum transport. Rev. Mod. Phys. 69, 731–808 (1997).
Schuster, R. & Ensslin, K. Antidot superlattices: classical chaos and quantum transport. Adv. Solid State Phys. 34, 195–218 (1994).
Loss, D. & Goldbart, P. Period and amplitude halving in mesoscopic rings with spin. Phys. Rev. B 43, 13762–13765 (1991).
Acknowledgements
We thank M. Büttiker and D. Loss for valuable discussions. Financial support from the Swiss Science Foundation (Schweizerischer Nationalfonds) is gratefully acknowledged.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Fuhrer, A., Lüscher, S., Ihn, T. et al. Energy spectra of quantum rings. Nature 413, 822–825 (2001). https://doi.org/10.1038/35101552
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1038/35101552
This article is cited by
-
Enhancement of persistent currents and magnetic fields in a two dimensional quantum ring
Scientific Reports (2023)
-
Vortex structure in Wigner molecules
Scientific Reports (2023)
-
Theoretical modeling of magnetic field effects on the optical properties of type-II core–shell quantum dot
Applied Nanoscience (2023)
-
Optical absorption in concentric double quantum rings
Optical and Quantum Electronics (2023)
-
Susceptibility, entropy and specific heat of quantum rings in monolayer graphene: comparison between different entropy formalisms
Journal of Computational Electronics (2022)
Comments
By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.
