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Hole spin relaxation in Ge–Si core–shell nanowire qubits

Abstract

Controlling decoherence is the biggest challenge in efforts to develop quantum information hardware1,2,3. Single electron spins in gallium arsenide are a leading candidate among implementations of solid-state quantum bits, but their strong coupling to nuclear spins produces high decoherence rates4,5,6. Group IV semiconductors, on the other hand, have relatively low nuclear spin densities, making them an attractive platform for spin quantum bits. However, device fabrication remains a challenge, particularly with respect to the control of materials and interfaces7. Here, we demonstrate state preparation, pulsed gate control and charge-sensing spin readout of hole spins confined in a Ge–Si core–shell nanowire. With fast gating, we measure T1 spin relaxation times of up to 0.6 ms in coupled quantum dots at zero magnetic field. Relaxation time increases as the magnetic field is reduced, which is consistent with a spin–orbit mechanism that is usually masked by hyperfine contributions.

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Figure 1: Spin qubit device based on a Ge–Si heterostructure nanowire.
Figure 2: Zeeman splitting of confined holes in a single quantum dot.
Figure 3: Hole-spin doublets in a Ge–Si double dot.
Figure 4: Pulsed gate measurements of spin relaxation times.

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References

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

    Article  CAS  Google Scholar 

  2. Hanson, R. & Awschalom, D. Coherent manipulation of single spins in semiconductors. Nature 453, 1043–1049 (2008).

    Article  CAS  Google Scholar 

  3. Petta, J. R., Lu, H. & Gossard, A. C. A coherent beam splitter for electronic spin states. Science 327, 669–672 (2010).

    Article  CAS  Google Scholar 

  4. 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  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  7. Dyakonov, M. I. (ed.) Spin Physics in Semiconductors (Springer Series in Solid-State Sciences 157, Springer, 2008).

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

    Article  CAS  Google Scholar 

  9. Koppens, F., Buizert, C., Tielrooij, K. & Vink, I. Driven coherent oscillations of a single electron spin in a quantum dot. Nature 442, 766–771 (2006).

    Article  CAS  Google Scholar 

  10. Nowack, K., Koppens, F. & Nazarov, Y. Coherent control of a single electron spin with electric fields. Science 318, 1430–1433 (2007).

    Article  CAS  Google Scholar 

  11. Bluhm, H. et al. Dephasing time of GaAs electron–spin qubits coupled to a nuclear bath exceeding 200 µs. Nature Phys. 7, 109–113 (2011).

    Article  CAS  Google Scholar 

  12. Foletti, S., Bluhm, H., Mahalu, D., Umansky, V. & Yacoby, A. Universal quantum control of two-electron spin quantum bits using dynamic nuclear polarization. Nature Phys. 5, 903–908 (2009).

    Article  CAS  Google Scholar 

  13. Trauzettel, B., Bulaev, D. V., Loss, D. & Burkard, G. Spin qubits in graphene quantum dots. Nature Phys. 3, 192–196 (2007).

    Article  CAS  Google Scholar 

  14. Kloeffel, C., Trif, M. & Loss, D. Strong spin–orbit interaction and helical hole states in Ge/Si nanowires. Phys. Rev. B 84, 195314 (2011).

    Article  Google Scholar 

  15. Mason, N., Biercuk, M. & Marcus, C. Local gate control of a carbon nanotube double quantum dot. Science 303, 655–658 (2004).

    Article  CAS  Google Scholar 

  16. Hu, Y. et al. A Ge/Si heterostructure nanowire-based double quantum dot with integrated charge sensor. Nature Nanotech. 2, 622–625 (2007).

    Article  CAS  Google Scholar 

  17. Steele, G. A., Gotz, G. & Kouwenhoven, L. P. Tunable few-electron double quantum dots and Klein tunnelling in ultraclean carbon nanotubes. Nature Nanotech. 4, 363–367 (2009).

    Article  CAS  Google Scholar 

  18. Shaji, N. et al. Spin blockade and lifetime-enhanced transport in a few-electron Si/SiGe double quantum dot. Nature Phys. 4, 540–544 (2008).

    Article  CAS  Google Scholar 

  19. Katsaros, G. et al. Hybrid superconductor–semiconductor devices made from self-assembled SiGe nanocrystals on silicon. Nature Nanotech. 5, 458–464 (2010).

    Article  CAS  Google Scholar 

  20. Zwanenburg, F. A., van Rijmenam, C., Fang, Y., Lieber, C. M. & Kouwenhoven, L. P. Spin states of the first four holes in a silicon nanowire quantum dot. Nano Lett. 9, 1071–1079 (2009).

    Article  CAS  Google Scholar 

  21. Xiao, M., House, M. G. & Jiang, H. W. Measurement of the spin relaxation time of single electrons in a silicon metal-oxide–semiconductor-based quantum dot. Phys. Rev. Lett. 104, 096801 (2010).

    Article  CAS  Google Scholar 

  22. Simmons, C. B. et al. Tunable spin loading and T1 of a silicon spin qubit measured by single-shot readout. Phys. Rev. Lett. 106, 156804 (2011).

    Article  CAS  Google Scholar 

  23. Hayes, R. R. et al. Lifetime measurements T1 of electron spins in Si/SiGe quantum dots. Preprint at arXiv:0908.0173v1 (2009).

  24. Borselli, M. G. et al. Pauli spin blockade in undoped Si/SiGe two-electron quantum dots. Appl. Phys. Lett. 99, 063109 (2011).

    Article  Google Scholar 

  25. Hanson, R., Petta, J. R., Tarucha, S. & Vandersypen, L. M. K. Spins in few-electron quantum dots. Rev. Mod. Phys. 79, 1217–1265 (2007).

    Article  CAS  Google Scholar 

  26. Lieber, C. & Wang, Z. Functional nanowires. MRS Bull. 32, 99–108 (2007).

    Article  CAS  Google Scholar 

  27. Lu, W., Xiang, J., Timko, B., Wu, Y. & Lieber, C. One-dimensional hole gas in germanium/silicon nanowire heterostructures. Proc. Natl Acad. Sci. USA 102, 10046–10051 (2005).

    Article  CAS  Google Scholar 

  28. Zulicke, U. & Csontos, D. Zeeman splitting in cylindrical hole quantum wires. Curr. Appl. Phys. 8, 237–240 (2008).

    Article  Google Scholar 

  29. Nenashev, A. V., Dvurechenskii, A. V. & Zinovieva, A. F. Wave functions and g factor of holes in Ge/Si quantum dots. Phys. Rev. B 67, 205301 (2003).

    Article  Google Scholar 

  30. Zhong, Z. H., Fang, Y., Lu, W. & Lieber, C. M. Coherent single charge transport in molecular-scale silicon nanowires. Nano Lett. 5, 1143–1146 (2005).

    Article  CAS  Google Scholar 

  31. Roddaro, S. et al. Spin states of holes in Ge/Si nanowire quantum dots. Phys. Rev. Lett. 101, 186802 (2008).

    Article  CAS  Google Scholar 

  32. Wang, L., Shen, K., Sun, B. Y. & Wu, M. W. Singlet–triplet relaxation in multivalley silicon single quantum dots. Phys. Rev. B 81, 235326 (2010).

    Article  Google Scholar 

  33. Trif, M., Simon, P. & Loss, D. Relaxation of hole spins in quantum dots via two-phonon processes. Phys. Rev. Lett. 103, 106601 (2009).

    Article  Google Scholar 

  34. Levitov, L. S. & Rashba, E. I. Dynamical spin–electric coupling in a quantum dot. Phys. Rev. B 67, 115324 (2003).

    Article  Google Scholar 

  35. Shankar, S., Tyryshkin, A., He, J. & Lyon, S. Spin relaxation and coherence times for electrons at the Si/SiO2 interface. Phys. Rev. B 82, 195323 (2010).

    Article  Google Scholar 

  36. Winkler, R. in Spin–Orbit Coupling Effects in Two-Dimensional Electron and Hole Systems Ch. 3, 28 (Springer Tracts in Modern Physics 191, Springer, 2003).

  37. Hao, X. J. et al. Strong and tunable spin–orbit coupling of one-dimensional holes in Ge/Si core/shell nanowires. Nano Lett. 10, 2956–2960 (2010).

    Article  CAS  Google Scholar 

  38. Nadj-Perge, S., Frolov, S. M., Bakkers, E. P. A. M. & Kouwenhoven, L. P. Spin–orbit qubit in a semiconductor nanowire. Nature 468, 1084–1087 (2010).

    Article  CAS  Google Scholar 

  39. Tang, J-M., Levy, J. & Flatté, M. E. All-electrical control of single ion spins in a semiconductor. Phys. Rev. Lett. 97, 106803 (2006).

    Article  Google Scholar 

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Acknowledgements

The authors thank H. Churchill, J. Medford and E. Rashba for technical help and discussions, and acknowledge support from the DARPA/QuEST programme.

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Contributions

Y.H. and F.K. performed the experiments. Y.H. prepared the materials and fabricated the devices. Y.H., F.K., C.M.L. and C.M.M. analysed the data and co-wrote the paper. All authors discussed the results and commented on the manuscript.

Corresponding authors

Correspondence to Charles M. Lieber or Charles M. Marcus.

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The authors declare no competing financial interests.

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Hu, Y., Kuemmeth, F., Lieber, C. et al. Hole spin relaxation in Ge–Si core–shell nanowire qubits. Nature Nanotech 7, 47–50 (2012). https://doi.org/10.1038/nnano.2011.234

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