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Register a new userDirect mapping of the formation of a persistent spin helix: Supplementary information
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The spin-orbit interaction (SOI) in zincblende semiconductor quantum wells can be set to a symmetry point, in which spin decay is strongly suppressed for a helical spin mode. Signatures of such a persistent spin helix (PSH) have been probed using the transient spin grating technique, but it has not yet been possible to observe the formation and the helical nature of a PSH. Here we directly map the diffusive evolution of a local spin excitation into a helical spin mode by a time- and spatially resolved magneto-optical Kerr rotation technique. Depending on its in-plane direction, an external magnetic field interacts differently with the spin mode and either highlights its helical nature or destroys the SU(2) symmetry of the SOI and thus decreases the spin lifetime. All relevant SOI parameters are experimentally determined and confirmed with a numerical simulation of spin diffusion in the presence of SOI.
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We study the lifetime of the persistent spin helix in semiconductor quantum wells with equal Rashba- and linear Dresselhaus spin-orbit interactions. In order to address the temperature dependence of the relevant spin relaxation mechanisms we derive and solve semiclassical spin diffusion equations taking into account spin-dependent impurity scattering, cubic Dresselhaus spin-orbit interactions and the effect of electron-electron interactions. For the experimentally relevant regime we find that the lifetime of the persistent spin helix is mainly determined by the interplay of cubic Dresselhaus spin-orbit interaction and electron-electron interactions. We propose that even longer lifetimes can be achieved by generating a spatially damped spin profile instead of the persistent spin helix state.
The spin orbit interaction plays a crucial role in diverse fields of condensed matter, including the investigation of Majorana fermions, topological insulators, quantum information and spintronics. In III V zinc blende semiconductor heterostructures, two types of spin orbit interaction, Rashba and Dresselhaus act on the electron spin as effective magnetic fields with different directions. They are characterized by coefficients alpha and beta, respectively. When alpha is equal to beta, the so called persistent spin helix symmetry is realized. In this condition, invariance with respect to spin rotations is achieved even in the presence of the spin orbit interaction, implying strongly enhanced spin lifetimes for spatially periodic spin modes. Existing methods to evaluate alpha/beta require fitting analyses that often include ambiguity in the parameters used. Here, we experimentally demonstrate a simple and fitting parameter free technique to determine alpha/beta and to deduce the absolute values of alpha and beta. The method is based on the detection of the effective magnetic field direction and the strength induced by the two spin orbit interactions. Moreover, we observe the persistent spin helix symmetry by gate tuning.
We experimentally investigate the dynamics of a persistent spin helix in etched GaAs wire structures of 2 to 80 um width. Using magneto-optical Kerr rotation with high spatial resolution, we determine the lifetime of the spin helix. A few nanoseconds after locally injecting spin polarization into the wire, the polarization is strongly enhanced as compared to the two-dimensional case. This is mostly attributed to a transition to one-dimensional diffusion, strongly suppressing diffusive dilution of spin polarization. The intrinsic lifetime of the helical mode is only weakly increased, which indicates that the channel confinement can only partially suppress the cubic Dresselhaus spin-orbit interaction.
We study the phase diagram of the interacting two-dimensional electron gas (2DEG) with equal Rashba and Dresselhaus spin-orbit coupling, which for weak coupling gives rise to the well-known persistent spin-helix phase. We construct the full Hartree-Fock phase diagram using a classical Monte-Carlo method analogous to that used in Phys.Rev.B 96, 235425 (2017). For the 2DEG with only Rashba spin-orbit coupling, it was found that at intermediate values of the Wigner-Seitz radius rs the system is characterized by a single Fermi surface with an out-of-plane spin polarization, while at slightly larger values of rs it undergoes a transition to a state with a shifted Fermi surface and an in-plane spin polarization. The various phase transitions are first-order, and this shows up in discontinuities in the conductivity and the appearance of anisotropic resistance in the in-plane polarized phase. In this work, we show that the out-of-plane spin-polarized region shrinks as the strength of the Dresselhaus spin-orbit interaction increases, and entirely vanishes when the Rashba and Dresselhaus spin-orbit coupling strengths are equal. At this point, the system can be mapped onto a 2DEG without spin-orbit coupling, and this transformation reveals the existence of an in-plane spin-polarized phase with a single, displaced Fermi surface beyond rs > 2.01. This is confirmed by classical Monte-Carlo simulations. We discuss experimental observation and useful applications of the novel phase, as well as caveats of using the classical Monte-Carlo method.
Time-resolved Kerr-rotation microscopy explores the influence of optical doping on the persistent spin helix in a [001]-grown CdTe quantum well at cryogenic temperatures. Electron spin diffusion dynamics reveal a momentum-dependent effective magnetic field providing SU(2) spin-rotation symmetry, consistent with kinetic theory. The Dresselhaus and Rashba spin-orbit coupling parameters are extracted independently from rotating the spin helix with external magnetic fields applied parallel and perpendicular to the effective magnetic field. Most importantly, a non-uniform spatiotemporal precession pattern is observed. The kinetic theory framework of spin diffusion allows for modeling of this finding by incorporating the photocarrier density into the Rashba ($alpha$) and the Dresselhaus ($beta_3$) parameters. Corresponding calculations are further validated by an excitation-density dependent measurement. This work shows universality of the persistent spin helix by its observation in a II-VI compound and the ability to fine-tune it by optical doping.
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