Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Emergence of the persistent spin helix in semiconductor quantum wells

Abstract

According to Noether’s theorem1, for every symmetry in nature there is a corresponding conservation law. For example, invariance with respect to spatial translation corresponds to conservation of momentum. In another well-known example, invariance with respect to rotation of the electron’s spin, or SU(2) symmetry, leads to conservation of spin polarization. For electrons in a solid, this symmetry is ordinarily broken by spin–orbit coupling, allowing spin angular momentum to flow to orbital angular momentum. However, it has recently been predicted that SU(2) can be achieved in a two-dimensional electron gas, despite the presence of spin–orbit coupling2. The corresponding conserved quantities include the amplitude and phase of a helical spin density wave termed the ‘persistent spin helix’2. SU(2) is realized, in principle, when the strengths of two dominant spin–orbit interactions, the Rashba3 (strength parameterized by α) and linear Dresselhaus4 (β1) interactions, are equal. This symmetry is predicted to be robust against all forms of spin-independent scattering, including electron–electron interactions, but is broken by the cubic Dresselhaus term (β3) and spin-dependent scattering. When these terms are negligible, the distance over which spin information can propagate is predicted to diverge as α approaches β1. Here we report experimental observation of the emergence of the persistent spin helix in GaAs quantum wells by independently tuning α and β1. Using transient spin-grating spectroscopy5, we find a spin-lifetime enhancement of two orders of magnitude near the symmetry point. Excellent quantitative agreement with theory across a wide range of sample parameters allows us to obtain an absolute measure of all relevant spin–orbit terms, identifying β3 as the main SU(2)-violating term in our samples. The tunable suppression of spin relaxation demonstrated in this work is well suited for application to spintronics6,7.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Figure 1: Double-exponential decay of transient spin gratings.
Figure 2: Rashba and linear Dresselhaus tuning.
Figure 3: Temperature dependence of the PSH.

References

  1. 1

    Noether, E. Invariante Variationsprobleme. Nachr. König. Gesellsch. Wiss. Göttingen, Math-Phys. Klasse 235–257 (1918)

  2. 2

    Bernevig, B. A., Orenstein, J. & Zhang, S.-C. Exact SU(2) symmetry and persistent spin helix in a spin-orbit coupled system. Phys. Rev. Lett. 97, 236601 (2006)

    ADS  Article  Google Scholar 

  3. 3

    Bychkov, Y. A. & Rashba, E. I. Oscillatory effects and the magnetic susceptibility of carriers in inversion layers. J. Phys. Chem. 17, 6039–6045 (1984)

    Google Scholar 

  4. 4

    Dresselhaus, G. Spin–orbit coupling effects in zinc blende structures. Phys. Rev. 100, 580–586 (1955)

    ADS  CAS  Article  Google Scholar 

  5. 5

    Cameron, A. R., Riblet, P. & Miller, A. Spin gratings and the measurement of electron drift mobility in multiple quantum well semiconductors. Phys. Rev. Lett. 76, 4793–4796 (1996)

    ADS  CAS  Article  Google Scholar 

  6. 6

    Awschalom, D. D., Loss, D. & Samarth, N. (eds) Semiconductor Spintronics and Quantum Computation (Springer, 2002)

    Book  Google Scholar 

  7. 7

    Ohno, M. & Yoh, K. Datta-Das-type spin-field-effect transistor in the nonballistic regime. Phys. Rev. B 77, 045323 (2008)

    ADS  Article  Google Scholar 

  8. 8

    Meier, F. & Zakharchenya, B. Optical Orientation (North-Holland, 1984)

    Google Scholar 

  9. 9

    Gedik, N. & Orenstein, J. Absolute phase measurement in heterodyne detection of transient gratings. Opt. Lett. 29, 2109–2111 (2004)

    ADS  Article  Google Scholar 

  10. 10

    Crooker, S. A., Awschalom, D. D. & Samarth, N. Time-resolved Faraday rotation spectroscopy of spin dynamics in digital magnetic heterostructures. IEEE J. Sel. Top. Quantum Electron. 1, 1082–1092 (1995)

    ADS  CAS  Article  Google Scholar 

  11. 11

    Froltsov, V. A. Diffusion of inhomogeneous spin distribution in a magnetic field parallel to interfaces of a III–V semiconductor quantum well. Phys. Rev. B 64, 045311 (2001)

    ADS  Article  Google Scholar 

  12. 12

    Burkov, A. A., Nunez, A. S. & MacDonald, A. H. Theory of spin-charge-coupled transport in a two-dimensional electron gas with Rashba spin-orbit interactions. Phys. Rev. B 70, 155308 (2004)

    ADS  Article  Google Scholar 

  13. 13

    Weber, C. P. et al. Nondiffusive spin dynamics in a two-dimensional electron gas. Phys. Rev. Lett. 98, 076604 (2007)

    ADS  CAS  Article  Google Scholar 

  14. 14

    Schliemann, J., Egues, J. C. & Loss, D. Nonballistic spin-field-effect transistor. Phys. Rev. Lett. 90, 146801 (2003)

    ADS  Article  Google Scholar 

  15. 15

    Stanescu, T. D. & Galitski, V. Spin relaxation in a generic two-dimensional spin-orbit coupled system. Phys. Rev. B 75, 125307 (2007)

    ADS  Article  Google Scholar 

  16. 16

    Braun, W. Trampert, A. Däweritz, L. & Ploog, K. H. Nonuniform segregation of Ga at AlAs/GaAs heterointerfaces. Phys. Rev. B 55, 1689–1695 (1997)

    ADS  MathSciNet  CAS  Article  Google Scholar 

  17. 17

    de Andrada e Silva, E. A. La Rocca, G. C. & Bassani, F. Spin-orbit splitting of electronic states in semiconductor asymmetric quantum wells. Phys. Rev. B 55, 16293–16299 (1997)

    ADS  CAS  Article  Google Scholar 

  18. 18

    Schubert, E. F. et al. Fermi-level-pinning-induced impurity redistribution in semiconductors during epitaxial growth. Phys. Rev. B 42, 1364–1368 (1990)

    ADS  CAS  Article  Google Scholar 

  19. 19

    Winkler, R. Spin–Orbit Coupling Effects in Two-Dimensional Electron and Hole Systems (Springer Tracts Mod. Phys. Vol. 191, Springer, 2003)

    Book  Google Scholar 

  20. 20

    Krich, J. J. & Halperin, B. I. Cubic Dresselhaus spin-orbit coupling in 2D electron quantum dots. Phys. Rev. Lett. 98, 226802 (2007)

    ADS  Article  Google Scholar 

  21. 21

    Chantis, A. N., Schilfgaarde, M. & Kotani, T. Ab initio prediction of conduction band spin splitting in zinc blende semiconductors. Phys. Rev. Lett. 96, 086405 (2006)

    ADS  Article  Google Scholar 

  22. 22

    Fabian, J., Matos-Abiague, A., Ertler, C., Stano, P. & Zutic, I. Semiconductor spintronics. Acta Physica Slovaca 57, 565–907 (2007)

    ADS  CAS  Google Scholar 

  23. 23

    D’Amico, I. & Vignale, G. Spin Coulomb drag in the two-dimensional electron liquid. Phys. Rev. B 68, 045307 (2003)

    ADS  Article  Google Scholar 

  24. 24

    Weber, C. P. et al. Observation of spin Coulomb drag in a two-dimensional electron gas. Nature 437, 1330–1333 (2005)

    ADS  CAS  Article  Google Scholar 

  25. 25

    Weng, M. Q., Wu, M. W. & Cui, H. L. Spin relaxation in n-type GaAs quantum wells with transient spin grating. J. Appl. Phys. 103, 063714 (2008)

    ADS  Article  Google Scholar 

  26. 26

    Sherman, E. & Ya Random spin–orbit coupling and spin relaxation in symmetric quantum wells. Appl. Phys. Lett. 82, 209–211 (2003)

    ADS  CAS  Article  Google Scholar 

  27. 27

    D’Yakonov, M. I. & Perel’, V. I. Spin relaxation of conduction electrons in noncentrosymmetric semiconductors. Sov. Phys. Solid State 13, 3023–3026 (1971)

    Google Scholar 

Download references

Acknowledgements

Work performed at Lawrence Berkeley National Laboratory and Stanford University was supported by the US Department of Energy, Office of Basic Energy Science, Materials Science and Engineering Division, and at the University of California, Santa Barbara by the US National Science Foundation and Office of Naval Research. S.M. acknowledges partial support through the National Defense Science and Engineering Graduate Fellowship Program. We thank J. Stephens and J. Krich for discussions, G. Fleming for use of a phase-mask array, and K. Bruns for creating the PSH diagram of Fig. 1c.

Author information

Affiliations

Authors

Corresponding author

Correspondence to J. D. Koralek.

Supplementary information

Supplementary Information

This file contains Supplementary Notes to Supplementary Figures S1-S7 with Legends and Supplementary Tables S3 and S4. (PDF 535 kb)

PowerPoint slides

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Koralek, J., Weber, C., Orenstein, J. et al. Emergence of the persistent spin helix in semiconductor quantum wells. Nature 458, 610–613 (2009). https://doi.org/10.1038/nature07871

Download citation

Further reading

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.

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing