Direct determination of spin-orbit interaction coefficients and realization of the persistent spin helix symmetry

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.