Spin Accumulation in Diffusive Conductors with Rashba and Dresselhaus Spin-Orbit Interaction

Abstract

We calculate the electrically induced spin accumulation in diffusive systems due to both Rashba (with strength $\alpha )$ and Dresselhaus (with strength $\beta )$ 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, $\alpha =\pm \beta$. In thermodynamically large systems, the finite spin accumulation predicted by Chaplik, Entin and Magarill, [Physica E {\bf 13}, 744 (2002)] and by Trushin and Schliemann [Phys. Rev. B {\bf 75}, 155323 (2007)] is recovered an infinitesimally small distance away from the singular point $\alpha =\pm \beta$. 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 $\gamma$, or (iii) for finite frequency measurements. We obtain the parametric range over which the magnetoelectric effect is suppressed in these three instances as (i) $|\alpha |-|\beta |\lesssim 1/mL$, (ii)$|\alpha |-|\beta |\lesssim \gamma p_{\mathrm{F}}^2$, and (iii) $|α|-|β| \lesssiM \sqrt{ω/m p_{\rm F}\ell}$ with $\ell$ the elastic mean free path and $p_{\mathrm{F}}$ the Fermi momentum. We attribute the absence of spin accumulation close to $\alpha =\pm \beta$ to the underlying U (1) symmetry. We illustrate and confirm our predictions numerically.

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• Recursive Green's function method for multi-terminal nanostructures
• Anomalous spin precession and spin Hall effect in semiconductor quantum wells
• Functional Approach to Electrodynamics of Media
• Spin transistor action from Onsager reciprocity and SU(2) gauge theory
• Geometric Correlations and Breakdown of Mesoscopic Universality in Spin Transport
• Efficient spin accumulation carried by slow relaxons in chiral tellurium
• Effects of scattering area shape on spin conductance in a four-terminal spin-Hall setup