 Theory of spin transport in an $n$typed GaAs quantum well
M.W. Wu and M.Q. Weng Dept. of Physics, Univ. of Science & Technology of China, CN
Keywords: spintronics, spin transport, dephasing, decoherence
Abstract: We perform a manybody investigation of the spin
diffusion/transport in an $n$doped GaAs QW based on a set of
manybody kinetic transport equations. These equations are derived for
the spatial inhomogeneous system by using nonequilibrium Green
function method with generalized KadanoffBaym Ansatz in a
twospinband model\cite{wu1,wu2,wu3}. Our theory takes all
the inhomogeneous broadening effect, the spin diffusion due to the
spacial inhomogeneity and the spin dephasing/decoherence into account and gets the
results selfconsistently.
We reexamine the wildly adopted quasi independent electron model
(QIEM)\cite{schmidt,spintronics,flatte_prl_2000,zutic_0106085,zutic}
and pointed out an important
manybody spin decoherence effect which is missing in the single
electron model. The new decoherence effect is based on interference
effect of electrons/spins with different momentum ${\bf k}$ along the
diffusion direction, which is referred as ``inhomogeneous broadening effect'' in
our paper. We have shown that this inhomogeneous broadening effect can
cause the spin decoherence alone even without the scattering and that
the resulting decoherence can be more important than the dephasing
effect due to DP term together with the scattering part. Our study
shows the inadequacy of the QIEM. Therefore, it is important to use
the full manybody theory to study the spin transport.
We further study the spin diffusion/transport from the full
manybody theory with the DP terms (The spin dephasing mechanism for
$n$typed GaAs QW at high temperature is the DP mechanism.) and the
scattering included. By numerically solving the kinetic Bloch
equations, together with the Poisson equation, we are able to
investigate the spin diffusion in the steady state under the constant
spin injection. We have shown the spin diffusion in the
absence/presence of an applied electric field along the diffusion direction as
well as with/without impurities. By applying an electric field along
the diffusion direction, one gets much longer spin diffusion length as
the electrons are driven by the electric field and get a net drift
velocity. Also in the presence of the electric field, the spin
diffusion length is reduced if one introduces impurities into the
sample. However, when there is no applied electric field, the spin
diffusion length is {\em enlarged} by adding impurities into the
sample. This is contrary to what is predicted by the QIEM. The reason
of this qualitative difference is also discussed. We also
study the effects of the magnetic field in the Voigt configuration and
the applied electric fields along the QW growth direction to the spin
diffusion. In the present of the magnetic field, the spin
polarization exhibits oscillation along the direction of
diffusion and the decay due to the interference is much more effective than that of the
dephasing and therefore the spin diffusion length is greatly reduced.
We also investigate the spin diffusion at different temperatures.
We find that as the temperature increases, the interference effect
reduces as the electron distribution near $k_x=0$, which is main
contributor to the inhomogeneous broadening, becomes smaller. As a result, the spin
diffusion length increases with the temperature. We show that
the applied electric field along the growth direction makes the Rashba
term more pronounced and hence both the decoherence and the dephasing
get enlarged. Consequently the diffusion length is reduced.
We have also demonstrated the time evolution of the diffusion of a spin
package. The spin signals near the center of the package always decay
with time due to the diffusion as well as the dephasing. Whereas the
spin signals away from the center first increase then drop. For
positions beyond the regime of the initial spin package, the spin polarization can
be opposite to the initial one due to the spin flipping by the
relatively large local effective magnetic field originated from the DP
term together with the spin coherence $\rho_{\sigma\sigma}$, with the later coming from
both the diffusion and the spin precession. We also predict the spin
oscillations with time at some positions. These features cannot be
obtained from the QIEM.
NSTI Nanotech 2003 Conference Technical Program Abstract
