Energy spectra of quantum rings


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.

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Figure 1: Sample layout.
Figure 2: The addition spectrum.
Figure 3: Reconstruction of the energy spectrum.
Figure 4: Addition spectrum of a Sinai billiard.


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We thank M. Büttiker and D. Loss for valuable discussions. Financial support from the Swiss Science Foundation (Schweizerischer Nationalfonds) is gratefully acknowledged.

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Correspondence to K. Ensslin.

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Fuhrer, A., Lüscher, S., Ihn, T. et al. Energy spectra of quantum rings. Nature 413, 822–825 (2001).

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