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 (SO) coupling, allowing spin angular momentum to flow to orbital angular momentum. However, it has recently been predicted that SU(2) can be recovered in a two-dimensional electron gas (2DEG), despite the presence of SO coupling. 2 The corresponding conserved quantities include the amplitude and phase of a helical spin density wave termed the "persistent spin helix" (PSH) . 2 SU(2) is restored, in principle, when the strength of two dominant SO interactions, the Rashba 3 (α) and linear Dresselhaus 4 (β 1 ), 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 → β 1 . Here we observe experimentally the emergence of the PSH in GaAs quantum wells (QW's) by independently tuning α and β 1 . Using transient spin-grating spectroscopy 5 (TSG), 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 SO 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. 6, 7 SLAC-PUB-13935 SIMES,

Reducing the heat generated in traditional electronics is a chief motivation for the development of spin-based electronics, called spintronics. Spin-based transistors that do not strictly rely on the raising or lowering of electrostatic barriers can overcome scaling limits in charge-based transistors. Spin transport in semiconductors might also lead to dissipation-less information transfer with pure spin currents. Despite these thermodynamic advantages, little experimental literature exists on the thermal aspects of spin transport in solids. A recent and surprising exception was the discovery of the spin-Seebeck effect, reported as a measurement of a redistribution of spins along the length of a sample of permalloy (NiFe) induced by a temperature gradient. This macroscopic spatial distribution of spins is, surprisingly, many orders of magnitude larger than the spin diffusion length, which has generated strong interest in the thermal aspects of spin transport. Here, the spin-Seebeck effect is observed in a ferromagnetic semiconductor, GaMnAs, which allows flexible design of the magnetization directions, a larger spin polarization, and measurements across the magnetic phase transition. This effect is observed even in the absence of longitudinal charge transport. The spatial distribution of spin currents is maintained across electrical breaks, highlighting the local nature of this thermally driven effect.

Electronic states in disordered conductors on the verge of localization are predicted to exhibit critical spatial characteristics indicative of the proximity to a metal-insulator phase transition. We have used scanning tunneling microscopy to visualize electronic states in Ga 1-x Mn x As samples close to this transition. Our measurements show that doping-induced disorder produces strong spatial variations in the local tunneling conductance across a wide range of energies. Near the Fermi energy, where spectroscopic signatures of electron-electron interaction are the most prominent, the electronic states exhibit a diverging spatial correlation length. Power-law decay of the spatial correlations is accompanied by log-normal distributions of the local density of states and multifractal spatial characteristics. Our method can be used to explore critical correlations in other materials close to a quantum critical point.Since Anderson first proposed that disorder could localize electrons in solids fifty years ago (1), studies of the transition between extended and localized quantum states have been at the forefront of physics (2). Realizations of Anderson localization occur in a wide range of physical systems from seismic waves to ultracold atomic gases, in