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.

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

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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.

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Correspondence to J. D. Koralek.

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

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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

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