**"Emergence of the persistent spin helix in semiconductor quantum wells"**

J. D. Koralek: C. P. Weber, J. Orenstein, B. A. Bernevig, Shou-Cheng Zhang, S. Mack & D. D. Awschalom; Nature , 04/02/09.

**Abstract**:

According to Noether’s theorem^{1}, 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 coupling^{2}. 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 Rashba^{3} (strength parameterized by ) and linear Dresselhaus^{4} ( _{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 ( _{3}) and spin-dependent scattering. When these terms are negligible, the distance over which spin information can propagate is predicted to diverge as approaches _{1}. Here we report experimental observation of the emergence of the persistent spin helix in GaAs quantum wells by independently tuning and _{1}. Using transient spin-grating spectroscopy^{5}, 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 _{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^{6, }^{7}.