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Spin qubits in graphene quantum dots

Nature Physics volume 3, pages 192–196 (2007)Cite this article

Abstract

The main characteristics of good qubits are long coherence times in combination with fast operating times. It is well known that carbon-based materials could increase the coherence times of spin qubits, which are among the most developed solid-state qubits. Here, we propose how to form spin qubits in graphene quantum dots. A crucial requirement to achieve this goal is to find quantum-dot states where the usual valley degeneracy in bulk graphene is lifted. We show that this problem can be avoided in quantum dots based on ribbons of graphene with armchair boundaries. The most remarkable new feature of the proposed spin qubits is that, in an array of many qubits, it is possible to couple any two of them via Heisenberg exchange with the others being decoupled by detuning. This unique feature is a direct consequence of the quasi-relativistic spectrum of graphene.

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Figure 1: Schematic diagram of a graphene double quantum dot.
Figure 2: Bound-state solutions for two different dot sizes.
Figure 3: Energy bands for single- and double-dot case.
Figure 4: Ground-state wavefunction.
Figure 5: Long-distance coupling of two qubit ground states.
Figure 6: Triple-quantum-dot set-up.

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References

  1. Loss, D. & DiVincenzo, D. P. Quantum computation with quantum dots. Phys. Rev. A 57, 120–126 (1998).

    Article  ADS  Google Scholar 

  2. Elzerman, J. M. et al. Single-shot read-out of an individual electron spin in a quantum dot. Nature 430, 431–435 (2004).

    Article  ADS  Google Scholar 

  3. Hanson, R. et al. Single-shot readout of electron spin states in a quantum dot using spin-dependent tunnel rates. Phys. Rev. Lett. 94, 196802 (2005).

    Article  ADS  Google Scholar 

  4. Petta, J. R. et al. Coherent manipulation of coupled electron spins in semiconductor quantum dots. Science 309, 2180–2184 (2005).

    Article  ADS  Google Scholar 

  5. Koppens, F. H. L. et al. Driven coherent oscillations of a single electron spin in a quantum dot. Nature 442, 766–771 (2006).

    Article  ADS  Google Scholar 

  6. Khaetskii, A. V. & Nazarov, Y. V. Spin relaxation in semiconductor quantum dots. Phys. Rev. B 61, 12639–12642 (2000).

    Article  ADS  Google Scholar 

  7. Khaetskii, A. V. & Nazarov, Y. V. Spin-flip transitions between Zeeman sublevels in semiconductor quantum dots. Phys. Rev. B 64, 125316 (2001).

    Article  ADS  Google Scholar 

  8. Golovach, V. N., Khaetskii, A. V. & Loss, D. Phonon-induced decay of the electron spin in quantum dots. Phys. Rev. Lett. 93, 016601 (2004).

    Article  ADS  Google Scholar 

  9. Burkard, G., Loss, D. & DiVincenzo, D. P. Coupled quantum dots as quantum gates. Phys. Rev. B 59, 2070–2078 (1999).

    Article  ADS  Google Scholar 

  10. Erlingsson, S. I., Nazarov, Y. V. & Fal’ko, V. I. Nucleus-mediated spin-flip transitions in GaAs quantum dots. Phys. Rev. B 64, 195306 (2001).

    Article  ADS  Google Scholar 

  11. Khaetskii, A. V., Loss, D. & Glazman, L. Electron spin decoherence in quantum dots due to interaction with nuclei. Phys. Rev. Lett. 88, 186802 (2002).

    Article  ADS  Google Scholar 

  12. Coish, W. A. & Loss, D. Hyperfine interaction in a quantum dot: Non-Markovian electron spin dynamics. Phys. Rev. B 70, 195340 (2004).

    Article  ADS  Google Scholar 

  13. Johnson, A. C. et al. Triplet–singlet spin relaxation via nuclei in a double quantum dot. Nature 435, 925–928 (2005).

    Article  ADS  Google Scholar 

  14. Koppens, F. H. L. et al. Control and detection of singlet-triplet mixing in a random nuclear field. Science 309, 1346–1350 (2005).

    Article  ADS  Google Scholar 

  15. Min, H. et al. Intrinsic and Rashba spin-orbit interactions in graphene sheets. Phys. Rev. B 74, 165310 (2006).

    Article  ADS  Google Scholar 

  16. Novoselov, K. S. et al. Electric field effect in atomically thin carbon films. Science 306, 666–669 (2004).

    Article  ADS  Google Scholar 

  17. Novoselov, K. S. et al. Two-dimensional gas of massless Dirac fermions in graphene. Nature 438, 197–200 (2005).

    Article  ADS  Google Scholar 

  18. Zhang, Y., Tan, Y.-W., Stormer, H. L. & Kim, P. Experimental observation of the quantum Hall effect and Berry’s phase in graphene. Nature 438, 201–204 (2005).

    Article  ADS  Google Scholar 

  19. Cheianov, V. V. & Fal’ko, V. I. Selective transmission of Dirac electrons and ballistic magnetoresistance of n–p junctions in graphene. Phys. Rev. B 74, 041403R (2006).

    Article  ADS  Google Scholar 

  20. Dombay, N. & Calogeracos, A. Seventy years of the Klein paradox. Phys. Rep. 315, 41–58 (1999).

    Article  ADS  Google Scholar 

  21. Katsnelson, M. I., Novoselov, K. S. & Geim, A. K. Klein paradox in graphene. Nature Phys. 2, 620–625 (2006).

    Article  ADS  Google Scholar 

  22. McClure, J. W. Diamagnetism of graphite. Phys. Rev. 104, 666–671 (1956).

    Article  ADS  Google Scholar 

  23. Semenoff, G. W. Condensed-matter simulation of a three-dimensional anomaly. Phys. Rev. Lett. 53, 2449–2452 (1984).

    Article  ADS  Google Scholar 

  24. DiVincenzo, D. P. & Mele, E. J. Self-consistent effective-mass theory for intralayer screening in graphite intercalation compounds. Phys. Rev. B 29, 1685–1694 (1984).

    Article  ADS  Google Scholar 

  25. Silvestrov, P. G. & Efetov, K. B. Quantum dots in graphene. Phys. Rev. Lett. 98, 016802 (2007).

    Article  ADS  Google Scholar 

  26. Nilsson, J., Castro Neto, A. H., Guinea, F. & Peres, N. M. R. Transmission through a biased graphene bilayer barrier. Preprint at <http://www.arxiv.org/cond-mat/0607343> (2006).

  27. De Martino, A., Dell’Anna, L. & Egger, R. Magnetic confinement of massless Dirac fermions in graphene. Preprint at <http://www.arxiv.org/cond-mat/0610290> (2006).

  28. Brey, L. & Fertig, H. A. Electronic states of graphene nanoribbons studied with the Dirac equation. Phys. Rev. B 73, 235411 (2006).

    Article  ADS  Google Scholar 

  29. Tworzydło, J., Trauzettel, B., Titov, M., Rycerz, A. & Beenakker, C. W. J. Quantum-limited shot noise in graphene. Phys. Rev. Lett. 96, 246802 (2006).

    Article  ADS  Google Scholar 

  30. Grabert, H. & Devoret, M. H. (eds) Single Charge Tunnelling (Plenum, New York, 1991).

  31. Svore, K. M., Terhal, B. M. & DiVincenzo, D. P. Local fault-tolerant quantum computation. Phys. Rev. A 72, 022317 (2005).

    Article  ADS  Google Scholar 

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Acknowledgements

We thank H. A. Fertig and L. M. K. Vandersypen for discussions and acknowledge support from the Swiss NSF, NCCR Nanoscience, DARPA, ONR and JST ICORP.

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Authors and Affiliations

  1. Department of Physics and Astronomy, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland

    Björn Trauzettel, Denis V. Bulaev, Daniel Loss & Guido Burkard

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  1. Björn Trauzettel
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  2. Denis V. Bulaev
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  3. Daniel Loss
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  4. Guido Burkard
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Correspondence to Guido Burkard.

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The authors declare no competing financial interests.

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Trauzettel, B., Bulaev, D., Loss, D. et al. Spin qubits in graphene quantum dots. Nature Phys 3, 192–196 (2007). https://doi.org/10.1038/nphys544

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