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.

We have examined the newly proposed method in order to electrically deduce the ratio between the Rashba and Dresselhaus spin–orbit interaction (SOI) parameters. Anisotropic magneto-conductance in gate-fitted InGaAs narrow wires is observed under an in-plane magnetic field. From the comparison between experiments and calculated Rashba SOI parameters, we have found that the method is applicable only when the wire width is shorter than the spin precession length. A transition from narrow wires to two-dimensional (2D) wires is observed both by decreasing the spin precession length and by increasing wire width.

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