Spin helix modes in 2D and 1D
Spin-orbit interaction induces an effective magnetic field. The direction of this field depends on the electron momentum. The spin precession about this field typically leads to a rapid dephasing of electron spins in a 2D system. By tuning the spin-orbit interaction to a special symmetry, a situation can be achieved where the spins collectively precess about a single axis and form a helical spin patterned, called a persistent spin helix [1,2].
Using spatially resolved pump-probe measurements, we have imaged the formation of a persistent spin helix that develops from a local spin excitation . Using a magnetic field along the direction of the spin-orbit field, we can observe the precession of the helix, which yields a direct visualization of the helical nature of the spin mode.
By confining a 2D electron gas into a 1D wire geometry, we can gradually switch off the spin dephasing mechanism. Thus we can form a helical spin mode without the need to tune the spin-orbit symmetry [4,5]. For narrow wires in the diffusive regime, cubic Dresselhaus contributions limit the spin lifetime.
 J. Schliemann, J. C. Egues, and D. Loss, “Nonballistic Spin-Field-Effect Transistor,” Phys. Rev. Lett. 90, 146801 (2003).
 B. Andrei Bernevig, J. Orenstein, and Shou-Cheng Zhang, “Exact SU(2) Symmetry and Persistent Spin Helix in a Spin-Orbit Coupled System,” Phys. Rev. Lett. 97, 236601 (2006).
 M. P. Walser, C. Reichl, W. Wegscheider and G. Salis, “Direct mapping of the formation of a persistent spin helix,” Nature Phys. 8, 757 (2012).
 P. Altmann, M. P. Walser, C. Reichl, W. Wegscheider and G. Salis, “ Suppressed decay of a laterally confined persistent spin helix,” Phys. Rev. B 90, 201306(R) (2014).
 P. Altmann, M. Kohda, C. Reichl, W. Wegscheider and G. Salis, “Transition of a two-dimensional spin mode to a helical state by lateral confinement,” Phys. Rev. B 92, 235304 (2015).
Spatial maps of spin polarization in a two-dimensional electron gas recorded at three different times (10, 240 and 840 ps) after excitation of a local spin polarization at x=y=0 µm. The diffusively expanding spin polarization develops a stripe pattern, signature of the persistent spin helix.
Evolution of spin polarization in an unstructured 2D electron gas (a) compared with a wire of width 700 nm (b). Cross sections show the Bessel mode for 2D (c) and a helical mode for 1D (d).