TY - JOUR

T1 - Emergence of the persistent spin helix in semiconductor quantum wells

AU - Koralek, J. D.

AU - Weber, C. P.

AU - Orenstein, J.

AU - Bernevig, B. A.

AU - Zhang, Shou Cheng

AU - MacK, S.

AU - Awschalom, D. D.

N1 - Funding Information:
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.

PY - 2009/4/2

Y1 - 2009/4/2

N2 - According to Noethers theorem, 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 electrons 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 coupling. The corresponding conserved quantities include the amplitude and phase of a helical spin density wave termed the persistent spin helix. SU(2) is realized, in principle, when the strengths of two dominant spin-orbit interactions, the Rashba (strength parameterized by α) and linear Dresselhaus (Β 1) 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 (Β 3) and spin-dependent scattering. When these terms are negligible, the distance over which spin information can propagate is predicted to diverge as α approaches Β 1. Here we report experimental observation of the emergence of the persistent spin helix in GaAs quantum wells by independently tuning α and Β 1. Using transient spin-grating spectroscopy, 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 Β 3 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 spintronics.

AB - According to Noethers theorem, 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 electrons 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 coupling. The corresponding conserved quantities include the amplitude and phase of a helical spin density wave termed the persistent spin helix. SU(2) is realized, in principle, when the strengths of two dominant spin-orbit interactions, the Rashba (strength parameterized by α) and linear Dresselhaus (Β 1) 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 (Β 3) and spin-dependent scattering. When these terms are negligible, the distance over which spin information can propagate is predicted to diverge as α approaches Β 1. Here we report experimental observation of the emergence of the persistent spin helix in GaAs quantum wells by independently tuning α and Β 1. Using transient spin-grating spectroscopy, 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 Β 3 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 spintronics.

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U2 - 10.1038/nature07871

DO - 10.1038/nature07871

M3 - Article

C2 - 19340077

AN - SCOPUS:63849227336

VL - 458

SP - 610

EP - 613

JO - Nature

JF - Nature

SN - 0028-0836

IS - 7238

ER -