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start slides for the Max Planck Institute

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1 parent bdb128d commit b0002ae1052792d632218a853a59d1dbaeb75af5 @moritz committed Feb 11, 2010
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  1. +50 −0 slides/gliederung
  2. +232 −0 slides/mpi.tex
  3. BIN slides/rashba-dispersion.jpg
  4. BIN slides/sample-leads.pdf
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+1. Motivation
+ What for?
+ quantum computations
+ low-power transistor
+ Why spins?
+ low decay rates
+ little power consumption
+ intrinsic QM property
+ Prior art
+ ferromagnetic materials
+ + very good spin separation
+# TODO: picture of hard disk; Giant magneto resistance
+ - hard to handle technologically
+ - metals => unwanted Schottky junctions
+ - not tunable
+ => unusable in CPUs
+
+2. Basics
+ Rashba Spin-Orbit Interaction
+ From Dirac equation
+ in solids: gap smaller => larger effect
+ k-dependent SO-coupling
+ Fisher-Lee relation
+ Green's Functions
+# TODO: picture excitation + response
+ Fisher-Lee relation
+ discretization
+
+3. Setup: Interface at an angle
+ Analytical calculations
+ Khodas' approach
+ critical effects
+ but only in chiral basis
+ adapting to z-direction
+ Numeric calculations
+ enumerating sites
+ matrix sizes
+ interfaces
+
+4. Results
+ Rough agreement simulation <=> analytical calculation
+ difference: number of modes, effective model
+ Some spin separation survives (20% max)
+
+5. Summary
+ Spins are very interesting for quantum comptuation
+ Non-magnetic materials necessary for future scaling
+ Rashba SO-coupling: critical filtration in chiral basis
+ Up to 20% survive in non-chiral basis
+
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+\documentclass{beamer}
+
+\mode<presentation>
+{
+ \usetheme{Montpellier}
+ % oder ...
+
+ \setbeamercovered{transparent}
+ % oder auch nicht
+}
+
+\usepackage{array}
+\usepackage[normalem]{ulem}
+\usepackage{fancyvrb,verbatim}
+\setlength{\extrarowheight}{2mm}
+
+%\usepackage[german]{babel}
+%%\usepackage{ngerman}
+% oder was auch immer
+
+\usepackage[utf8]{inputenc}
+% oder was auch immer
+
+\usepackage{multicol}
+
+\usepackage{times}
+\usepackage[T1]{fontenc}
+% Oder was auch immer. Zu beachten ist, das Font und Encoding passen
+% müssen. Falls T1 nicht funktioniert, kann man versuchen, die Zeile
+% mit fontenc zu löschen.
+
+\usepackage{calc}
+
+\title{Ballistic Transport of Spin-Polarized Electron Beams in Mesoscopic
+Systems}
+
+%\subtitle
+%{Untertitel nur angeben, wenn es einen im Tagungsband gibt}
+
+\author{Moritz Lenz}
+\institute{Institut für Theoretische Physik und Astrophysik, Universität
+Würzburg}
+\date{Max Planck Institut, 2010-02-foo}
+
+\subject{Physics}
+
+
+% Falls eine Logodatei namens "university-logo-filename.xxx" vorhanden
+% ist, wobei xxx ein von latex bzw. pdflatex lesbares Graphikformat
+% ist, so kann man wie folgt ein Logo einfügen:
+
+% \pgfdeclareimage[height=2.0cm]{university-logo}{Heriot-Watt_University}
+% \logo{\pgfuseimage{university-logo}}
+
+
+
+% Folgendes sollte gelöscht werden, wenn man nicht am Anfang jedes
+% Unterabschnitts die Gliederung nochmal sehen möchte.
+%\AtBeginSubsection[]
+%{
+% \begin{frame}<beamer>
+% \frametitle{Gliederung}
+% \tableofcontents[currentsection,currentsubsection]
+% \end{frame}
+%}
+
+
+% Falls Aufzählungen immer schrittweise gezeigt werden sollen, kann
+% folgendes Kommando benutzt werden:
+
+%\beamerdefaultoverlayspecification{<+->}
+
+
+
+\begin{document}
+
+\begin{frame}
+ \titlepage
+
+ \begin{center}
+{
+ \large Diploma Thesis\\[2em]
+}
+ Supervisor: Prof. Ewelina Hankiewicz
+
+\end{center}
+
+% \begin{multicols}{2}
+% \includegraphics[width=0.4\textwidth]{setup-79_reduced.jpg}
+%
+%{ \tiny Graphics from
+% http://www.quantumlah.org/images/
+% setup-79\_800x600.jpg}
+% \end{multicols}
+
+\end{frame}
+
+\section{Motivation}
+
+\begin{frame}
+ \frametitle{Motivation - Why spin manipulation}
+
+ \begin{itemize}
+ \item Spin states can encode information
+ \item Spin states stay coherent much longer than charge states
+ \item Now moving required to change state
+ \item Less heat dissipation
+ \end{itemize}
+
+\end{frame}
+
+\subsection{Prior Art}
+
+\begin{frame}{Motivation - Prior Art}
+ \textbf{Spin manipulation with ferromagnetic materials}
+
+ \begin{itemize}
+ \item Very successful (GMR)
+ \item Good ideas (Datta-Das spin transistor)
+ \end{itemize}
+\end{frame}
+
+\begin{frame}{Motivation - Prior Art}
+ \textbf{Why investigate alternatives?}
+
+ \begin{itemize}
+ \item Technologically hard to handle
+ \item Limits in scaling down
+ \item Static effects only
+ \item Ferromagnetic materials are metals
+ $\Rightarrow$ Schottky junctions when mixing with semiconductors
+ \end{itemize}
+\end{frame}
+
+\subsection{Non-magnetic semiconductors}
+\begin{frame}{Motivation - Alternatives}
+ \textbf{Spin manipulation in non-magnetic semiconductors}
+
+ \begin{itemize}
+ \item Well-known techniques applicable
+ \item Asymmetry tunable by electric fields
+ \item Analogy to optics
+ \end{itemize}
+\end{frame}
+
+\section{Theory}
+\subsection{Relativistic quantum theory}
+\begin{frame}{Theory: Pauli Equation}
+ Relativistic QM in vacuum
+
+ \begin{align*}
+ \left( \frac{\vec p^2}{2m}- \frac{e\hbar \ \vec\sigma \cdot (\vec p \times \vec E)}
+ {2\Delta} +\ldots\right)\Psi = E \Psi
+ \end{align*}
+
+ \begin{align*}
+ \Delta\qquad & 2m_e c^2\\
+ \vec \sigma \qquad & \textnormal{Pauli matrices}\\
+ \vec p \qquad & \textnormal{momentum}\\
+ \vec E \qquad & \textnormal{electric field}\\
+ \end{align*}
+
+\end{frame}
+
+\subsection{Rasbha spin-orbit coupling}
+
+\begin{frame}{Theory: Bychkov-Rashba term}
+ In Solids
+
+ \begin{align*}
+ H = \frac{\vec p^2}{2 m^*} + \alpha (\vec I \times \vec \sigma) \cdot
+ \vec p
+ \end{align*}
+
+ \begin{align*}
+ \alpha \qquad & \textnormal{SO-coupling strength}\\
+ \vec I \qquad & \textnormal{Unit vector of asymmetry}
+ \end{align*}
+
+\end{frame}
+
+\begin{frame}{Theory: Dispersion relation and Rashba}
+
+ \begin{multicols}{2}
+ \includegraphics[height=6cm]{rashba-dispersion.jpg}
+
+ \begin{align*}
+ E(k) = \frac{\hbar^2}{2 m^*} k^2 \pm \alpha k
+ \end{align*}
+
+ Energy depends on spin and momentum $\Rightarrow$ manipulable\\[1em]
+
+ $\alpha$ tunable through external electric field.
+\end{multicols}
+\end{frame}
+
+\subsection{Landauer Formula}
+
+\begin{frame}{Theory: Landauer Formula}
+ \begin{multicols}{2}
+ \includegraphics[width=6cm]{sample-leads}
+
+ \begin{align*}
+ G = \frac{2 e^2}{h} MT
+ \end{align*}
+
+ \begin{align*}
+ G \qquad& \textnormal{conductance}\\
+ M \qquad& \textnormal{number of modes}\\
+ T \qquad& \textnormal{transmission propability}
+ \end{align*}
+ \end{multicols}
+\end{frame}
+
+\begin{frame}{Theory: Green's Function formalism}
+ \begin{multicols}{2}
+ \includegraphics[width=6cm]{sample-leads}
+
+ \begin{align*}
+ G = \frac{2 e^2}{h} MT
+ \end{align*}
+
+ \begin{align*}
+ G \qquad& \textnormal{conductance}\\
+ M \qquad& \textnormal{number of modes}\\
+ T \qquad& \textnormal{transmission propability}
+ \end{align*}
+ \end{multicols}
+\end{frame}
+
+
+\end{document}
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