Spin accumulation in diffusive conductors with Rashba and Dresselhaus spin-orbit interaction

We calculate the electrically induced spin accumulation in diffusive systems due to both Rashba (with strength α) and Dresselhaus (with strength β) spin-orbit interaction. Using a diffusion equation approach we find that magnetoelectric effects disappear and that there is thus no spin accumulation when both interactions have the same strength, α=±β. In thermodynamically large systems, the finite spin accumulation predicted by Chaplik, Entin, and Magarill [Physica E 13, 744 (2002)] and by Trushin and Schliemann [Phys. Rev. B 75, 155323 (2007)] is recovered an infinitesimally small distance away from the singular point α=±β. We show however that the singularity is broadened and that the suppression of spin accumulation becomes physically relevant (i) in finite-sized systems of size L, (ii) in the presence of a cubic Dresselhaus interaction of strength γ, or (iii) for finite-frequency measurements. We obtain the parametric range over which the magnetoelectric effect is suppressed in these three instances as (i) |α|−|β|≲1/mL, (ii) |α|−|β|≲γp2F, and (iii) |α|−|β|≲√ω/mpFℓ with ℓ the elastic mean-free path and pF the Fermi momentum. We attribute the absence of spin accumulation close to α=±β to the underlying U(1) symmetry. We illustrate and confirm our predictions numerically.