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Direct mapping of the formation of a persistent spin helix


The spin–orbit interaction (SOI) in zincblende semiconductor quantum wells can be set to a symmetry point, in which spin decay is strongly suppressed for a helical spin mode. Signatures of such a persistent spin helix (PSH) have been probed using the transient spin-grating technique, but it has not yet been possible to observe the formation and the helical nature of a PSH. Here we directly map the diffusive evolution of a local spin excitation into a helical spin mode by a time-resolved and spatially resolved magneto-optical Kerr rotation technique. Depending on its in-plane direction, an external magnetic field interacts differently with the spin mode and either highlights its helical nature or destroys the SU(2) symmetry of the SOI and thus decreases the spin lifetime. All relevant SOI parameters are experimentally determined and confirmed with a numerical simulation of spin diffusion in the presence of SOI.

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Figure 1: Direct mapping of the PSH formation.
Figure 2: Helical spin modes and the PSH.
Figure 3: Spin diffusion and SOI characterization.
Figure 4: Dependence of the total magnetic field Btot on k.
Figure 5: Interplay of the PSH with an external magnetic field.
Figure 6: Detuning from the PSH regime.


  1. Winkler, R. Spin-Orbit Coupling Effects in Two-Dimensional Electron and Hole Systems (Springer, 2003).

    Book  Google Scholar 

  2. Dyakonov, M. I. (ed.) in Spin Physics in Semiconductors (Springer, 2008).

  3. König, M. et al. Quantum spin Hall insulator state in HgTe quantum wells. Science 318, 766–770 (2007).

    ADS  Article  Google Scholar 

  4. Sau, J. D., Lutchyn, R. M., Tewari, S. & Das Sarma, S. Generic new platform for topological quantum computation using semiconductor heterostructures. Phys. Rev. Lett. 104, 040502 (2010).

    ADS  Article  Google Scholar 

  5. Mourik, V. et al. Signatures of Majorana fermions in hybrid superconductor- semiconductor nanowire devices. Science 336, 1003–1007 (2012).

    ADS  Article  Google Scholar 

  6. Koralek, J. D. et al. Emergence of the persistent spin helix in semiconductor quantum wells. Nature 458, 610–613 (2009).

    ADS  Article  Google Scholar 

  7. Nitta, J., Akazaki, T., Takayanagi, H. & Enoki, T. Gate control of spin-orbit interaction in an inverted In0.53Ga0.47As/In0.52Al0.48As heterostructure. Phys. Rev. Lett. 78, 1335–1338 (1997).

    ADS  Article  Google Scholar 

  8. Studer, M., Salis, G., Ensslin, K., Driscoll, D. C. & Gossard, A. C. Gate-controlled spin-orbit interaction in a parabolic GaAs/AlGaAs quantum well. Phys. Rev. Lett. 103, 027201 (2009).

    ADS  Article  Google Scholar 

  9. D’yakonov, M. I. & Perel’, V. I. Spin relaxation of conduction electrons in noncentrosymmetric semiconductors. Sov. Phys. Solid State 13, 3023–3026 (1972).

    Google Scholar 

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

    ADS  Article  Google Scholar 

  11. 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 

  12. Wunderlich, J. et al. Spin Hall effect transistor. Science 330, 1801–1804 (2010).

    ADS  Article  Google Scholar 

  13. Duckheim, M. & Loss, D. Resonant spin polarization and spin current in a two-dimensional electron gas. Phys. Rev. B 75, 201305(R) (2007).

    ADS  Article  Google Scholar 

  14. D’Amico, I. & Vignale, G. Theory of spin Coulomb drag in spin-polarized transport. Phys. Rev. B 62, 4853–4857 (2000).

    ADS  Article  Google Scholar 

  15. Yang, L. et al. Doppler velocimetry of spin propagation in a two-dimensional electron gas. Nature Phys. 8, 153–157 (2012).

    ADS  Article  Google Scholar 

  16. Yang, L., Orenstein, J. & Lee, D-H. Random walk approach to spin dynamics in a two-dimensional electron gas with spin–orbit coupling. Phys. Rev. B 82, 155324 (2010).

    ADS  Article  Google Scholar 

  17. Stephens, J. et al. Spin accumulation in forward-biased MnAs/GaAs Schottky diodes. Phys. Rev. Lett. 93, 097602 (2004).

    ADS  Article  Google Scholar 

  18. Crooker, S. A. & Smith, D. L. Imaging spin flows in semiconductors subject to electric, magnetic, and strain fields. Phys. Rev. Lett. 94, 236601 (2005).

    ADS  Article  Google Scholar 

  19. Meier, L. et al. Measurement of Rashba and Dresselhaus spin-orbit magnetic fields. Nature Phys. 3, 650–654 (2007).

    ADS  Article  Google Scholar 

  20. Ryan, J. F. et al. Time-resolved photoluminescence of two-dimensional hot carriers in GaAs–AlGaAs heterostructures. Phys. Rev. Lett. 53, 1841–1844 (1984).

    ADS  Article  Google Scholar 

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We would like to acknowledge financial support from the Swiss National Science Foundation through NCCR Nano and NCCR QSIT, as well as valuable discussions with R. Allenspach, K. Ensslin and Y. Chen.

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M.P.W. and G.S. designed the experiment, interpreted the data and wrote the manuscript. M.P.W. performed the time-resolved experiment. C.R. and W.W. grew the samples. G.S. performed numerical simulations.

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Correspondence to G. Salis.

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The authors declare no competing financial interests.

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Walser, M., Reichl, C., Wegscheider, W. et al. Direct mapping of the formation of a persistent spin helix. Nature Phys 8, 757–762 (2012).

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