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Controllable valley splitting in silicon quantum devices


Silicon has many attractive properties for quantum computing, and the quantum-dot architecture is appealing because of its controllability and scalability. However, the multiple valleys in the silicon conduction band are potentially a serious source of decoherence for spin-based quantum-dot qubits. Only when a large energy splits these valleys do we obtain well-defined and long-lived spin states appropriate for quantum computing. Here, we show that the small valley splittings observed in previous experiments on Si–SiGe heterostructures result from atomic steps at the quantum-well interface. Lateral confinement in a quantum point contact limits the electron wavefunctions to several steps, and enhances the valley splitting substantially, up to 1.5 meV. The combination of electrostatic and magnetic confinement produces a valley splitting larger than the spin splitting, which is controllable over a wide range. These results improve the outlook for realizing spin qubits with long coherence times in silicon-based devices.

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Figure 1: Quantum point contact.
Figure 2: Step transitions.
Figure 3: Valley splitting.
Figure 4: Comparison of valley and spin excitations.
Figure 5: Microwave spectroscopy of the valley splitting in a Si–SiGe Hall bar.


  1. Cirac, J. & Zoller, P. Quantum computations with cold trapped ions. Phys. Rev. Lett. 74, 4091–4094 (1995).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  3. Ciorga, M. et al. Addition spectrum of a lateral dot from Coulomb and spin-blockade spectroscopy. Phys. Rev. B 61, R16315–R16318 (2000).

    Article  ADS  Google Scholar 

  4. Fujisawa, T., Austing, D. G., Tokura, Y., Hirayama, Y. & Tarucha, S. Allowed and forbidden transitions in artificial hydrogen and helium atoms. Nature 419, 278–281 (2002).

    Article  ADS  Google Scholar 

  5. 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 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  8. Shnirman, A., Schön, G. & Hermon, Z. Quantum manipulations of small Josephson junctions. Phys. Rev. Lett. 79, 2371–2374 (1997).

    Article  ADS  Google Scholar 

  9. Nielsen, M. & Chuang, I. Quantum Computation and Quantum Information (Cambridge Univ. Press, Cambridge, 2000).

    MATH  Google Scholar 

  10. Cerletti, V., Coish, W. A., Gywat, O. & Loss, D. Recipes for spin-based quantum computing. Nanotechnology 16, R27–R49 (2005).

    Article  Google Scholar 

  11. Kane, B. E. A silicon-based nuclear spin quantum computer. Nature 393, 133–137 (1998).

    Article  ADS  Google Scholar 

  12. Yablonovitch, E. et al. Optoelectronic quantum telecommunications based on spins in semiconductors. Proc. IEEE 91, 761–780 (2003).

    Article  Google Scholar 

  13. Schäffler, F. High-mobility Si and Ge structures. Semicond. Sci. Technol. 12, 1515–1549 (1997).

    Article  ADS  Google Scholar 

  14. Ando, T., Fowler, A. B. & Stern, F. Electronic properties of two-dimensional systems. Rev. Mod. Phys. 54, 437–672 (1982).

    Article  ADS  Google Scholar 

  15. Boykin, T. B. et al. Valley splitting in strained silicon quantum wells. Appl. Phys. Lett. 84, 115–117 (2004).

    Article  ADS  Google Scholar 

  16. Weitz, P., Haug, R. J., von Klitzing, K. & Schäffler, F. Tilted magnetic field studies of spin- and valley-splittings in Si/Si1−xGex heterostructures. Surf. Sci. 361/362, 542–546 (1996).

    Article  ADS  Google Scholar 

  17. Koester, S. J., Ismail, K. & Chu, J. O. Determination of spin- and valley-split energy levels in strained Si quantum wells. Semicond. Sci. Technol. 12, 384–388 (1997).

    Article  ADS  Google Scholar 

  18. Khrapai, V. S., Shashkin, A. A. & Dolgopolov, V. P. Strong enhancement of the valley splitting in a two-dimensional electron system in silicon. Phys. Rev. B 67, 113305 (2003).

    Article  ADS  Google Scholar 

  19. Lai, K. et al. Two-flux composite fermion series of the fractional quantum Hall states in strained Si. Phys. Rev. Lett. 93, 156805 (2004).

    Article  ADS  Google Scholar 

  20. Pudalov, V. M., Punnoose, A., Brunthaler, G., Prinz, A. & Bauer, G. Valley splitting in Si-inversion layers at low magnetic fields. Preprint at <> (2001).

  21. Dobers, M., von Klitzing, K., Schneider, J., Weimann, G. & Ploog, K. Electrical detection of nuclear magnetic resonance in GaAs–AlxGa1−xAs heterostructures. Phys. Rev. Lett. 61, 1650–1653 (1988).

    Article  ADS  Google Scholar 

  22. Ando, T. Valley splitting in the silicon inversion layer: Misorientation effects. Phys. Rev. B 19, 3089–3095 (1979).

    Article  ADS  Google Scholar 

  23. Friesen, M., Eriksson, M. A. & Coppersmith, S. N. Magnetic field dependence of valley splitting in realistic Si/SiGe quantum wells. Appl. Phys. Lett. 89, 202106 (2006).

    Article  ADS  Google Scholar 

  24. Kohn, W. in Solid State Physics Vol. 5 (eds Seitz, F. & Turnbull, D.) 257–319 (Academic, New York, 1957).

    Google Scholar 

  25. Koiller, B., Hu, X. & das Sarma, S. Exchange in silicon-based quantum computer architecture. Phys. Rev. Lett. 88, 027903 (2002).

    Article  ADS  Google Scholar 

  26. Van Wees, B. J. et al. Quantized conductance of point contacts in a two-dimensional electron gas. Phys. Rev. Lett. 60, 848–850 (1988).

    Article  ADS  Google Scholar 

  27. Van Wees, B. J. et al. Quantum ballistic and adiabatic electron transport studied with quantum point contacts. Phys. Rev. B 43, 12431–12453 (1991).

    Article  ADS  Google Scholar 

  28. Ohkawa, F. J. & Uemura, Y. Theory of valley splitting in an N-channel (100) inversion layer of Si III. Enhancement of splittings by many-body effects. J. Phys. Soc. Jpn 43, 925–932 (1977).

    Article  ADS  Google Scholar 

  29. Jiang, H. W. & Yablonovitch, E. Gate-controlled electron spin resonance in GaAs/AlxGa1−xAs heterostructures. Phys. Rev. B 64, 041307 (2001).

    Article  ADS  Google Scholar 

  30. Takashina, K., Ono, Y., Fujiwara, A., Takahashi, Y. & Hirayama, Y. Valley polarization in Si(100) at zero magnetic field. Phys. Rev. Lett. 96, 236801 (2006).

    Article  ADS  Google Scholar 

  31. Roberts, M. M. et al. Elastically relaxed free-standing strained-silicon nanomembranes. Nature Mater. 5, 388–393 (2006).

    Article  ADS  Google Scholar 

  32. Ismail, K., Arafa, M., Saenger, K. L., Chu, J. O. & Meyerson, B. S. Extremely high electron mobility in Si/SiGe modulation-doped heterostructures. Appl. Phys. Lett. 66, 1077–1079 (1995).

    Article  ADS  Google Scholar 

  33. Klein, L. J. et al. Coulomb blockade in a silicon/silicon-germanium two-dimensional electron gas quantum dot. Appl. Phys. Lett. 84, 4047–4049 (2004).

    Article  ADS  Google Scholar 

  34. Cronenwett, S. M. et al. Low-temperature fate of the 0. 7 structure in a point contact: A Kondo-like correlated state in an open system. Phys. Rev. Lett. 88, 226805 (2002).

    Article  ADS  Google Scholar 

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We gratefully acknowledge conversations with R. Blick. This work was supported by NSA/LPS under ARO contract number W911NF-04-1-0389, and by the National Science Foundation through the ITR programme (DMR-0325634) and the EMT programme (CCF-0523675).

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Authors and Affiliations



J.C. and P.M. provided the samples. S.G., K.S., L.M., J.T., and L.K. carried out the fabrication and measurements. M.F., C.T., R.J. and S.C. did the theoretical work. S.G., K.S., L.M., M.F., S.C. and M.E. analysed the data. M.F., R.J., D.W., S.C., M.F. and M.E. planned the project. M.F., K.S., S.C. and M.E. prepared the manuscript.

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Correspondence to Mark Friesen or Mark A. Eriksson.

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The authors declare no competing financial interests.

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Goswami, S., Slinker, K., Friesen, M. et al. Controllable valley splitting in silicon quantum devices. Nature Phys 3, 41–45 (2007).

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