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[tex] more intro and summary hacking

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1 parent f1b7d43 commit 2e161ca679def7f421002de5cf599e0f5f372803 @moritz committed Dec 17, 2009
Showing with 63 additions and 20 deletions.
  1. +3 −0 tex/.gitignore
  2. +15 −0 tex/bib.bib
  3. +14 −3 tex/intro.tex
  4. +9 −3 tex/numerics.tex
  5. +22 −14 tex/summary.tex
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3 tex/.gitignore
@@ -2,3 +2,6 @@
*.log
*.dvi
thesis.pdf
+thesis.bbl
+thesis.blg
+thesis.toc
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15 tex/bib.bib
@@ -205,3 +205,18 @@ @misc{mathias
}
+@article{SHE,
+author = {Kato, Y. K. and Myers, R. C. and Gossard, A. C. and Awschalom, D. D.},
+title = {{Observation of the Spin Hall Effect in Semiconductors}},
+journal = {Science},
+volume = {306},
+number = {5703},
+pages = {1910-1913},
+doi = {10.1126/science.1105514},
+year = {2004},
+abstract = {Electrically induced electron-spin polarization near the edges of a semiconductor channel was detected and imaged with the use of Kerr rotation microscopy. The polarization is out-of-plane and has opposite sign for the two edges, consistent with the predictions of the spin Hall effect. Measurements of unstrained gallium arsenide and strained indium gallium arsenide samples reveal that strain modifies spin accumulation at zero magnetic field. A weak dependence on crystal orientation for the strained samples suggests that the mechanism is the extrinsic spin Hall effect.
+},
+URL = {http://www.sciencemag.org/cgi/content/abstract/306/5703/1910},
+eprint = {http://www.sciencemag.org/cgi/reprint/306/5703/1910.pdf}
+}
+
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17 tex/intro.tex
@@ -42,9 +42,20 @@ \chapter{Introduction}
However, building ferromagnetic contacts or devices on
the nano scale is a serious technological challenge, and combining millions of
-ferromagnetic structures on a single device seems hardly possible.
-
-In this Diploma Thesis, we therefore investigate how a spin polarized electron
+ferromagnetic structures on a single device seems hardly possible. There is
+also a conceptual difficulty: due to the band structure mismatch between
+metallic ferromagnetic materials and semiconductors, additional interface
+effects (like in Schottky diodes) arise, which can seriously inhibit the
+usefulness of such devices.
+
+New hope for non-magnetic spintronic devices came from the experimental
+observation of the Spin-Hall Effect in 2004 \cite{SHE}. In analogy to the
+classical Hall effect, an electrical current causes a spin imbalance in
+lateral direction. Unlike the ordinary Hall effect, no magnetic field is
+required, but rather the spin assembly is caused by the band
+structure of the semiconductor hetereostructure, or by impurities.
+
+In this Diploma Thesis, we investigate how a spin polarized electron
beam can be achieved by using only non-magnetic materials. The Rashba
spin-orbit coupling, which arises from
asymmetric structures in certain semiconductors, can be used as a tunable
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12 tex/numerics.tex
@@ -560,14 +560,20 @@ \section{Relation to experiments}
of the spin-orbit coupling strength can be tuned by a gate electrode that is
located above the sample.
-In this experimental setup two things disagree with our model, which
+In this experimental setup two things are different than our model, which
means we can't compare experimental results directly with ours: firstly the
electron sees two interfaces (one on entering the stripe, one on leaving) and
secondly the electric field also introduces a potential barrier, which
scatters electrons too.
-The spin polarization can be measured via the Inverse Spin-Hall Effect
-\cite{ishe-ew,ISHE} as an electrical current.
+In analogy to the classical Hall Effect, the Spin-Hall Effect can lead to a
+spin imbalance in the transverse direction of the driven current.
+
+The reverse effect, the so-called \emph{inverted Spin-Hall Effect}, can in
+turn be used to drive an electrical current by a spin imbalance, and thusly
+make the spin imbalance accessible to electrical measurements
+\cite{ishe-ew,ISHE}. Alternatively the spin imbalance could be detected with
+optical means, by measuring the transmission of circularly polarized light.
%For $\phi > \phi_c$, the wave $\exp{i p_x^+ x}\exp{i p_z z} t_{++}\chi_{SO}^+$
%does not propagate, because $p_x^+$ is imaginary. That means that the relative
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36 tex/summary.tex
@@ -4,19 +4,22 @@ \chapter{Summary and Outlook}
We analyzed the possibilities of achieving spin polarization in a
non-magnetic, microscopic semiconductor. We found that an interface between
normal and Rashba spin-orbit coupling areas splits an electron beam into
-components with different chirality, and if the angle between the interface
+components with different chirality, and can be used to manipulate
+spin-polarized electron beams similarly to optical light in media with
+different optical densities.
+
+If the angle between the interface
and the incident beam exceeds a critical angle, the beam with $+$ chirality
-ceases to propagate. This effect can be used to achieve spin polarization.
+ceases to propagate. This effect can be used to obtain a spin imbalance.
-We modeled such a system analytically in order to obtain a good understanding
-for the physics, and in an extensible numerical simulation in order to have
+We modeled such a system analytically in order to get a good understanding
+of the physics, and in an extensible numerical simulation in order to have
maximal flexibility with the choice of parameters and system details.
We developed a method to compare the analytical and numerical results, and in
-that course we found that the measurable spin polarization is partially
-absorbed by fact that the
-interface separates electron waves by chirality, not by spin component
-in $z$-direction.
+that course we found that the measurable spin imbalance is partially
+damped by fact that the interface separates electron waves by chirality,
+not by spin component in $z$-direction.
We also discussed the experimental more accessible setup of two regions with
different, non-zero strengths of spin-orbit interaction, and found that such an
@@ -30,12 +33,8 @@ \chapter{Summary and Outlook}
similar (but slightly more complex) setups have been grown and etched in HgTe
quantum wells.
-Future work in this area could involve a four-band model which includes both
-the conductance and valance band for each spin direction, would
-allow more precises modeling of a particular semiconductor, and thus be of
-more help to experimentalists. Using more realistic and specific parameters
-would allow to make quantitative recommendations on which angle best to use
-for such an interface.
+Future work in this area could cover the experimental setup of having a strip
+of tunable spin-orbit interaction.
There is also another simple extension to our model that would help making
quantitative predictions: when the spin-orbit coupling in an area is tuned by
@@ -45,4 +44,13 @@ \chapter{Summary and Outlook}
enhance our understanding of the spin polarization, but is crucial for
obtaining quantitative predictions of the measured signals.
+Also in the experiments magnetic fields are used to focus beams in the
+sample, so magnetic field would be a worthwhile addition to our model.
+
+To incorporate more realistic parameters of a particular semiconductor,
+our model could be expanded to use four bands,
+the conductance and valance band for each spin direction. This would allow to
+make quantitative recommendations on best angle for such an interface.
+
+
% vim: ts=4 sw=4 expandtab spell spelllang=en_us tw=78

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