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 α and β, respectively. When α is equal to β, 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 α/β require fitting analyses that often include ambiguity in the parameters used. Here, we experimentally demonstrate a simple and fitting parameter-free technique to determine α/β and to deduce the absolute values of α and β. 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.