Abstract
We consider Rashba spin–orbit effects on spin transport driven by an electric field in semiconductor quantum wells. We derive spin diffusion equations that are valid when the mean free path and the Rashba spin–orbit interaction vary on length scales larger than the mean free path in the weak spin–orbit coupling limit. From these general diffusion equations, we derive boundary conditions between regions of different spin–orbit couplings. We show that spin injection is feasible when the electric field is perpendicular to the boundary between two regions. When the electric field is parallel to the boundary, spin injection only occurs when the mean free path changes within the boundary, in agreement with the recent work by Tserkovnyak et al (Preprint cond-mat/0610190).
Highlights
PII: S1367-2630(07)48878-4 © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft transition layer, resulting in a finite spin-density jump, when the transition layer thickness is reduced to zero
We present results for the boundary conditions when the electric field is perpendicular to the interface
We discuss the implications of these boundary conditions on spin injection and show that for a parallel electric field spin injection is only possible when the mean free path together with α vary within the boundary layer, while for the perpendicular field spin injection takes place even when the mean free path is uniform in the system
Summary
In the absence of disorder, the electrons in a homogeneous quantum well are described by the. We assume that the transition layer thickness d between the regions is larger than the mean free path l, but smaller than the spin precession length λ = ̄h2/m∗α, where m∗ is the electron effective mass, l d λ This requires a sufficiently weak SOI or a low mobility sample. For the simplest case, where both the mean free path and the spin–orbit coupling linearly change within the boundary layer: α(x) αr For this simplest system of a linear variation of the spin–orbit coupling and mobility and assuming that one uses the same electric fields in the two scenarios, 2 is more effective than 1 provided αl − αr > τl − τr , αl + αr τl + τr e.g. when the change in the spin–orbit coupling constant is larger than the change in mobility between the regions. We are crudely characterizing the spin-injection efficiency by the jump in spin density with respect to the bulk levels
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