diff --git a/tex/adapting-pic.pdf b/tex/adapting-pic.pdf
index 0134e5a..7c0f3b7 100644
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diff --git a/tex/adapting.svg b/tex/adapting.svg
index 3b4e030..04e0a45 100644
--- a/tex/adapting.svg
+++ b/tex/adapting.svg
@@ -28,15 +28,15 @@
inkscape:pageopacity="0.0"
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@@ -162,138 +162,6 @@
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\phi^+_{A,c}$ the momentum in $x$ direction $p_{x,A}$ is again
imaginary, just like if we had another interface to a normal region
left of the $A$ region.
-It follows the same $\ta$ dependency, namely $\phi^+_{c2} =
--\sin^{-1}(\ta_A - \sqrt{1+\ta_A^2})$.
+$p_{x,A}$ has the same structural dependence on $\ta_A$ as $p_{x,B}$
+has on $\ta_B$:
+
+\begin{align}
+ p_{x,A}^+ = \sqrt{ p_A^2 - p_z^2} = p \sqrt{(\sqrt{1+\ta_A^2} -
+ \ta_A)^2 - \sin^2 \phi^+}
+\end{align}
+
+It follows that $\phi^+_{c2}$ has a similar form as $\phi^+_{c1}$,
+namely $\phi^+_{c2} = -\sin^{-1}(\ta_A - \sqrt{1+\ta_A^2})$.
%
%\begin{figure}
diff --git a/tex/numerics.tex b/tex/numerics.tex
index 7493c79..88733b5 100644
--- a/tex/numerics.tex
+++ b/tex/numerics.tex
@@ -287,7 +287,14 @@ \subsection{Comparison to Analytical Results}
\begin{center}
\includegraphics[width=0.8\textwidth]{adapting-pic.pdf}
\end{center}
- \caption{Injecting one spin-up charge carrier into the system}
+ \caption{Injecting one spin-up charge carrier into the system notionally
+ splits up the wave into two wave functions with $+$ and $-$ chirality.
+ At the interface a part of the wave is scattered, and
+ $\mathbf{\psi^\pm}$
+ describe the injected and reflected wave functions left of the
+ interface. The transmitted fraction of the wave function is then
+ projected onto the $\uparrow,\downarrow$ bases when it reaches the right
+ lead.}
\end{figure}
% Since there is no dissipation in our model, and we assume that the mere
@@ -438,7 +445,7 @@ \subsection{Comparison to Analytical Results}
(figure \ref{fig:n-so-rel}).
To understand better why we don't get a very clear picture of the critical
-angle the numerical results, we look at \ref{eq:a-n-left} and for a moment
+angle, we look at \ref{eq:a-n-left} and for a moment
ignore the global phases that the $\exp$ functions provide, and obtain a
simplified expression for $a$ and $b$.
@@ -457,7 +464,7 @@ \subsection{Comparison to Analytical Results}
T_{2\uparrow,1\uparrow} &\approx \left|a \chi_{SO}^{+U} t_{++}
+ b \chi_{SO}^{-U} t_{--} \right|^2\nonumber\\
T_{2\downarrow,1\downarrow} &\approx \left|c \chi_{SO}^{-D} t_{--}
- + d \chi_{SO}^{+D} t_{--} \right|^2
+ + d \chi_{SO}^{+D} t_{++} \right|^2
\label{eq:simplfied-t}
\end{align}
@@ -533,11 +540,12 @@ \section{Relation to experiments}
\begin{center}
\includegraphics[width=0.7\textwidth]{beamsplitter2.jpg}
\end{center}
- \caption{Experimental realization of a beam splitter, with two
+ \caption{Experimental realization of a beam splitter in a HgTe/CdTe quantum
+ well, with two
collimating quantum point contact on top and bottom. In the middle
there is a strip at angle $\phi = 45^\circ$ where an electric field
can be applied by a gate. Image courtesy of M. Mühlbauer,
- Physikalisches Institut, Universität Würzburg}
+ Physikalisches Institut, Universität Würzburg\cite{mathias}}
\label{fig:experiment}
\end{figure}
@@ -545,7 +553,8 @@ \section{Relation to experiments}
in experiments. Figure \ref{fig:experiment} shows such a sample as produced
by the group of H. Buhmann in our department \cite{mathias}.
-It has two wide contacts on the left and right side, and two collimating point
+It consists of a two-dimensional electron gas in a HgTe/CdTe quantum well. It has
+two wide leads on the left and right side, and two collimating point quantum
contacts on the top and bottom. At an angle of $45^{\circ}$ there is a stripe
across the sample. Inside the strip the electric field, and thus the strength
of the spin-orbit coupling strength can be tuned by a gate electrode that is
@@ -558,7 +567,7 @@ \section{Relation to experiments}
scatters electrons too.
The spin polarization can be measured via the Inverse Spin-Hall Effect
-\cite{ISHE} as an electrical current.
+\cite{ishe-ew,ISHE} as an electrical current.
%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
diff --git a/tex/rashba-dispersion.jpg b/tex/rashba-dispersion.jpg
new file mode 100644
index 0000000..c121199
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diff --git a/tex/setup-simple.pdf b/tex/setup-simple.pdf
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diff --git a/tex/setup-simple.svg b/tex/setup-simple.svg
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diff --git a/tex/setup-two-so-regions.pdf b/tex/setup-two-so-regions.pdf
index 2364d64..a467a06 100644
Binary files a/tex/setup-two-so-regions.pdf and b/tex/setup-two-so-regions.pdf differ
diff --git a/tex/setup-two-so-regions.svg b/tex/setup-two-so-regions.svg
index e8bbd03..fa472c1 100644
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+++ b/tex/setup-two-so-regions.svg
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diff --git a/tex/summary.tex b/tex/summary.tex
index 6d0dc87..0c3f72b 100644
--- a/tex/summary.tex
+++ b/tex/summary.tex
@@ -26,6 +26,10 @@ \chapter{Summary and Outlook}
In both cases a large angle between the incident beam the interface is
essential for obtaining a decent spin polarization.
+We also pointed out that experimental realization is quite possible, and that
+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
diff --git a/tex/thesis.tex b/tex/thesis.tex
index 27c5549..c0d69fa 100644
--- a/tex/thesis.tex
+++ b/tex/thesis.tex
@@ -188,8 +188,6 @@ \section{Transmission and Green's Functions}
$\delta = \delta(x - x_0)$ to result in two waves propagating away from $x_0$,
so our ansatz is
-% TODO: explicit form of $H$
-
\begin{align}
G(x, x_0) = \begin{cases}
A^+ e^{i k(x-x_0) } \qquad \textnormal{ for } x > x_0 \\
@@ -370,6 +368,17 @@ \section{Rashba Spin-Orbit Coupling}
$m^*$ is the effective mass
and $\alpha$ denotes the strength of the spin-orbit coupling.
+\begin{figure}[tb]
+ \begin{center}
+ \includegraphics[height=0.5\textwidth]{rashba-dispersion.jpg}
+ \end{center}
+ \caption{The Rashba spin-orbit coupling lifts the spin degeneracy of the
+ dispersion relation $E(k)$for $k != 0$.
+ Image courtesy by M. Mühlbauer \cite{mathias}.
+ }
+ \label{fig:rashba-dispersion}
+\end{figure}
+
This effect lifts the degeneracy of spin-up and spin-down electrons for
$k \not= 0$:
@@ -380,7 +389,8 @@ \section{Rashba Spin-Orbit Coupling}
So the Rashba spin-orbit coupling splits the spin bands similarly as the Zeeman
effect of a
magnetic field, but it depends on the wave vector and does not come with the
-something that is equivalent to the Lorentz force of the magnetic field.
+something that is equivalent to the Lorentz force of the magnetic field (see
+figure \ref{fig:rashba-dispersion}) .
Since in equilibrium the same number of charge carries have the wave vectors
$k$ and $-k$, the Rashba spin-orbit coupling does not introduce a spin