Abstract
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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References
Winkler, R. Spin-Orbit Coupling Effects in Two-Dimensional Electron and Hole Systems (Springer, 2003).
Dyakonov, M. I. (ed.) in Spin Physics in Semiconductors (Springer, 2008).
König, M. et al. Quantum spin Hall insulator state in HgTe quantum wells. Science 318, 766–770 (2007).
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).
Mourik, V. et al. Signatures of Majorana fermions in hybrid superconductor- semiconductor nanowire devices. Science 336, 1003–1007 (2012).
Koralek, J. D. et al. Emergence of the persistent spin helix in semiconductor quantum wells. Nature 458, 610–613 (2009).
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).
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).
D’yakonov, M. I. & Perel’, V. I. Spin relaxation of conduction electrons in noncentrosymmetric semiconductors. Sov. Phys. Solid State 13, 3023–3026 (1972).
Schliemann, J., Egues, J. C. & Loss, D. Nonballistic spin-field-effect transistor. Phys. Rev. Lett. 90, 146801 (2003).
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).
Wunderlich, J. et al. Spin Hall effect transistor. Science 330, 1801–1804 (2010).
Duckheim, M. & Loss, D. Resonant spin polarization and spin current in a two-dimensional electron gas. Phys. Rev. B 75, 201305(R) (2007).
D’Amico, I. & Vignale, G. Theory of spin Coulomb drag in spin-polarized transport. Phys. Rev. B 62, 4853–4857 (2000).
Yang, L. et al. Doppler velocimetry of spin propagation in a two-dimensional electron gas. Nature Phys. 8, 153–157 (2012).
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).
Stephens, J. et al. Spin accumulation in forward-biased MnAs/GaAs Schottky diodes. Phys. Rev. Lett. 93, 097602 (2004).
Crooker, S. A. & Smith, D. L. Imaging spin flows in semiconductors subject to electric, magnetic, and strain fields. Phys. Rev. Lett. 94, 236601 (2005).
Meier, L. et al. Measurement of Rashba and Dresselhaus spin-orbit magnetic fields. Nature Phys. 3, 650–654 (2007).
Ryan, J. F. et al. Time-resolved photoluminescence of two-dimensional hot carriers in GaAs–AlGaAs heterostructures. Phys. Rev. Lett. 53, 1841–1844 (1984).
Acknowledgements
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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Walser, M., Reichl, C., Wegscheider, W. et al. Direct mapping of the formation of a persistent spin helix. Nature Phys 8, 757–762 (2012). https://doi.org/10.1038/nphys2383
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DOI: https://doi.org/10.1038/nphys2383
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