\Part[
    \eng{Condensed matter physics}
    \ger{Festkörperphysik}
    ]{cm}
    \TODO{Bonds, hybridized orbitals, tight binding}
\Section[
    \eng{Bravais lattice}
    \ger{Bravais-Gitter}
    ]{bravais}

    % \begin{ttext}
    %     \eng{

    %     }
    %     \ger{

    %     }
    % \end{ttext}

    \eng[bravais_table2]{In 2D, there are 5 different Bravais lattices}
    \ger[bravais_table2]{In 2D gibt es 5 verschiedene Bravais-Gitter}

    \eng[bravais_table3]{In 3D, there are 14 different Bravais lattices}
    \ger[bravais_table3]{In 3D gibt es 14 verschiedene Bravais-Gitter}

    \Eng[lattice_system]{Lattice system}
    \Ger[lattice_system]{Gittersystem}
    \Eng[crystal_family]{Crystal system}
    \Ger[crystal_family]{Kristall-system}
    \Eng[point_group]{Point group}
    \Ger[point_group]{Punktgruppe}
    \eng[bravais_lattices]{Bravais lattices}
    \ger[bravais_lattices]{Bravais Gitter}

    \newcommand\bvimg[1]{\begin{center}\includegraphics[width=0.1\textwidth]{img/bravais/#1.pdf}\end{center}}
    \renewcommand\tabularxcolumn[1]{m{#1}}
    \newcolumntype{Z}{>{\centering\let\newline\\\arraybackslash\hspace{0pt}}X}
    \begin{table}[H]
        \centering
        \caption{\gt{bravais_table2}}
        \label{tab:bravais2}
    
        \begin{adjustbox}{width=\textwidth}
        \begin{tabularx}{\textwidth}{||Z|c|Z|Z||}
            \hline
            \multirow{2}{*}{\GT{lattice_system}} & \multirow{2}{*}{\GT{point_group}} & \multicolumn{2}{c||}{5 \gt{bravais_lattices}} \\ \cline{3-4}
                                                 & & \GT{primitive} (p) & \GT{centered} (c) \\ \hline
            \GT{monoclinic} (m) & $\text{C}_\text{2}$   & \bvimg{mp} & \\ \hline
            \GT{orthorhombic} (o) & $\text{D}_\text{2}$ & \bvimg{op} & \bvimg{oc} \\ \hline
            \GT{tetragonal} (t) & $\text{D}_\text{4}$   & \bvimg{tp} & \\ \hline
            \GT{hexagonal} (h) & $\text{D}_\text{6}$    & \bvimg{hp} & \\ \hline
        \end{tabularx}
        \end{adjustbox}
    \end{table}
    


    \begin{table}[H]
        \centering
        \caption{\gt{bravais_table3}}
        \label{tab:bravais3}
    
        % \newcolumntype{g}{>{\columncolor[]{0.8}}}
        \begin{adjustbox}{width=\textwidth}
            % \begin{tabularx}{\textwidth}{|c|}
            %     asdfasdfadslfasdfaasdofiuapsdoifuapodisufpaoidsufpaoidsufpaoisdfaoisdfpaosidfupaoidsufpaoidsufpaoidsufpaoisdufpaoidsufpoaiudsfpioaspdoifuaposidufpaoisudpfoiaupsdoifupasodf \\
            %     asdfasdfadslfasdfaasdofiuapsdoifuapodisufpaoidsufpaoidsufpaoisdfaoisdfpaosidfupaoidsufpaoidsufpaoidsufpaoisdufpaoidsufpoaiudsfpioaspdoifuaposidufpaoisudpfoiaupsdoifupasodf \\
            % \end{tabularx}
            % \begin{tabular}{|c|}
            %     asdfasdfadslfasdfaasdofiuapsdoifuapodisufpaoidsufpaoidsufpaoisdfaoisdfpaosidfupaoidsufpaoidsufpaoidsufpaoisdufpaoidsufpoaiudsfpioaspdoifuaposidufpaoisudpfoiaupsdoifupasodf \\
            %     asdfasdfadslfasdfaasdofiuapsdoifuapodisufpaoidsufpaoidsufpaoisdfaoisdfpaosidfupaoidsufpaoidsufpaoidsufpaoisdufpaoidsufpoaiudsfpioaspdoifuaposidufpaoisudpfoiaupsdoifupasodf \\
            % \end{tabular}
            % \\
        \begin{tabularx}{\textwidth}{||Z|Z|c|Z|Z|Z|Z||}
            \hline
            \multirow{2}{*}{\GT{crystal_family}} & \multirow{2}{*}{\GT{lattice_system}} & \multirow{2}{*}{\GT{point_group}} & \multicolumn{4}{c||}{14 \gt{bravais_lattices}} \\ \cline{4-7}
                                                 & & & \GT{primitive} (P) & \GT{base_centered} (S) & \GT{body_centered} (I) & \GT{face_centered} (F) \\ \hline
            \multicolumn{2}{||c|}{\GT{triclinic} (a)} & $\text{C}_\text{i}$ & \bvimg{tP}  &  &  &  \\  \hline
            \multicolumn{2}{||c|}{\GT{monoclinic} (m)} & $\text{C}_\text{2h}$ & \bvimg{mP} & \bvimg{mS}  &  &  \\ \hline
            \multicolumn{2}{||c|}{\GT{orthorhombic} (o)} & $\text{D}_\text{2h}$ & \bvimg{oP} & \bvimg{oS} & \bvimg{oI} & \bvimg{oF} \\ \hline
            \multicolumn{2}{||c|}{\GT{tetragonal} (t)} & $\text{D}_\text{4h}$ & \bvimg{tP} &  & \bvimg{tI} & \\ \hline
            \multirow{2}{*}{\GT{hexagonal} (h)} & \GT{rhombohedral} & $\text{D}_\text{3d}$ & \bvimg{hR} &  &  & \\ \cline{2-7}
             & \GT{hexagonal} & $\text{D}_\text{6h}$ & \bvimg{hP} &  &  & \\ \hline
            \multicolumn{2}{||c|}{\GT{cubic} (c)} & $\text{O}_\text{h}$ & \bvimg{cP} &  & \bvimg{cI} & \bvimg{cF} \\ \hline
        \end{tabularx}
        \end{adjustbox}
    \end{table}
    \TODO{FCC, BCC, diamond/Zincblende wurtzize cell/lattice vectors}
    \TODO{primitive unit cell: contains one lattice point}\\

family of plane that are equivalent due to crystal symmetry
    \begin{formula}{miller}
        \desc{Miller index}{}{}
        \desc[german]{Millersche Indizes}{}{}
        \eq{
            (hkl) & \text{\GT{plane}}\\
            [hkl] & \text{\GT{direction}}\\
            \{hkl\} & \text{\GT{millerFamily}}
        }
    \end{formula}
    

\Section[
    \eng{Reciprocal lattice}
    \ger{Reziprokes Gitter}
    ]{reci}
    \begin{ttext}
        \eng{The reciprokal lattice is made up of all the wave vectors $\vec{k}$ that ressemble standing waves with the periodicity of the Bravais lattice.}
        \ger{Das rezioproke Gitter besteht aus dem dem Satz aller Wellenvektoren $\vec{k}$, die ebene Wellen mit der Periodizität des Bravais-Gitters ergeben.}
    \end{ttext}

    \begin{formula}{vectors}
        \desc{Reciprocal lattice vectors}{}{$a_i$ real-space lattice vectors, $V_c$ volume of the primitive lattice cell}
        \desc[german]{Reziproke Gittervektoren}{}{$a_i$ Bravais-Gitter Vektoren, $V_c$ Volumen der primitiven Gitterzelle}
        \eq{
            \vec{b_1} &= \frac{2\pi}{V_c} \vec{a_2} \times \vec{a_3} \\
            \vec{b_2} &= \frac{2\pi}{V_c} \vec{a_3} \times \vec{a_1} \\
            \vec{b_3} &= \frac{2\pi}{V_c} \vec{a_1} \times \vec{a_2}
        }
    \end{formula}

    \Subsection[
        \eng{Scattering processes}
        \ger{Streuprozesse}
        ]{scatter}
        \begin{formula}{matthiessen}
            \desc{Matthiessen's rule}{Approximation, only holds if the processes are independent of each other}{$\mu$ mobility, $\tau$ scattering time}
            \desc[german]{Matthiessensche Regel}{Näherung, nur gültig wenn die einzelnen Streuprozesse von einander unabhängig sind}{$\mu$ Moblitiät, $\tau$ Streuzeit}
            \eq{
                \frac{1}{\mu} &= \sum_{i = \textrm{\GT{\fqname}}} \frac{1}{\mu_i} \\
                \frac{1}{\tau} &= \sum_{i = \textrm{\GT{\fqname}}} \frac{1}{\tau_i}
            }
        \end{formula}
    

\Section[
    \eng{Free electron gas}
    \ger{Freies Elektronengase}
]{free_e_gas}
    \begin{ttext}
        \eng{Assumptions: electrons can move freely and independent of each other.}
        \ger{Annahmen: Elektronen bewegen sich frei und unabhänig voneinander.}
    \end{ttext}

    \begin{formula}{drift_velocity}
        \desc{Drift velocity}{Velocity component induced by an external force (eg. electric field)}{$v_\text{th}$ thermal velocity}
        \desc[german]{Driftgeschwindgkeit}{Geschwindigkeitskomponente durch eine externe Kraft (z.B. ein elektrisches Feld)}{$v_\text{th}$ thermische Geschwindigkeit}
        \eq{\vec{v}_\text{D} = \vec{v} - \vec{v}_\text{th}}
    \end{formula}

    \begin{formula}{mean_free_time}
        \desc{Mean free time}{}{}
        \desc[german]{Streuzeit}{}{}
        \eq{\tau}
    \end{formula}

    \begin{formula}{mean_free_path}
        \desc{Mean free path}{}{}
        \desc[german]{Mittlere freie Weglänge}{}{}
        \eq{\ell = \braket{v} \tau}
    \end{formula}

    \begin{formula}{mobility}
        \desc{Electrical mobility}{}{$q$ charge, $m$ mass}
        \desc[german]{Beweglichkeit}{}{$q$ Ladung, $m$ Masse}
        \eq{\mu = \frac{q \tau}{m}}
    \end{formula}

    \Subsection[
        \eng{Drude model}
        \ger{Drude-Modell}
        ]{drude}
        \begin{ttext}
            \eng{Classical model describing the transport properties of electrons in materials (metals):
                The material is assumed to be an ion lattice and with freely moving electrons (electron gas). The electrons are 
                accelerated by an electric field and decelerated through collisions with the lattice ions.
                The model disregards the Fermi-Dirac partition of the conducting electrons.
            }
            \ger{Ein klassisches Model zur Beschreibung der Transporteigenschaften von Elektronen in (v.a.) Metallen:
                Der Festkörper wird als Ionenkristall mit frei beweglichen Elektronen (Elektronengas). 
                Die Elektronen werden durch ein Elektrisches Feld $E$ beschleunigt und durch Stöße mit den Gitterionen gebremst.
                Das Modell vernachlässigt die Fermi-Dirac Verteilung der Leitungselektronen.
            }
        \end{ttext}
        \begin{formula}{motion}
            \desc{Equation of motion}{}{$v$ electron speed, $\vec{v}_\text{D}$ drift velocity, $\tau$ mean free time between collisions}
            \desc[german]{Bewegungsgleichung}{}{$v$ Elektronengeschwindigkeit, $\vec{v}_\text{D}$ Driftgeschwindigkeit, $\tau$ Stoßzeit}
            \eq{\masse \odv{\vec{v}}{t} + \frac{\masse}{\tau} \vec{v}_\text{D} = -e \vec{E}}
        \end{formula}
        \begin{formula}{current_density}
            \desc{Current density}{Ohm's law}{$n$ charge particle density}
            \desc[german]{Stromdichte}{Ohmsches Gesetz}{$n$ Ladungsträgerdichte}
            \eq{\vec{j} = -ne\vec{v}_\text{D} = ne\mu \vec{E}}
        \end{formula}
        \begin{formula}{conductivity}
            \desc{Drude-conductivity}{}{}
            \desc[german]{Drude-Leitfähigkeit}{}{}
            \eq{\sigma = \frac{\vec{j}}{\vec{E}} = \frac{e^2 \tau n}{\masse} = n e \mu}
        \end{formula}

    \Subsection[
        \eng{Sommerfeld model}
        \ger{Sommerfeld-Modell}
        ]{sommerfeld}
        \begin{ttext}
            \eng{Assumes a gas of free fermions underlying the pauli-exclusion principle. Only electrons in an energy range of $\kB T$ around the Fermi energy $\EFermi$ participate in scattering processes.}
            \ger{Annahme eines freien Fermionengases, welches dem Pauli-Prinzip unterliegt. Nur Elektronen in einem Energiebereich von $\kB T$ um die Fermi Energe $\EFermi$ nehmen an Streuprozessen teil.}
        \end{ttext}
        \begin{formula}{current_density}
            \desc{Current density}{}{}
            \desc[german]{Stromdichte}{}{}
            \eq{\vec{j} = -en\braket{v} = -e n \frac{\hbar}{\masse}\braket{\vec{k}} = -e \frac{1}{V} \sum_{\vec{k},\sigma} \frac{\hbar \vec{k}}{\masse}}
        \end{formula}
        \TODO{The formula for the conductivity is the same as in the drude model?}

    \Subsection[
        \eng{2D electron gas}
        \ger{2D Elektronengas}
        ]{2deg}

        \begin{ttext}
            \eng{Lower dimension gases can be obtained by restricting a 3D gas with infinetly high potential walls on a narrow area with the width $L$.}
            \ger{
                Niederdimensionale Elektronengase erhält man, wenn ein 3D Gas durch unendlich hohe Potentialwände auf einem schmalen Bereich mit Breite $L$ eingeschränkt wird.
            }
        \end{ttext}
        \begin{formula}{confinement_energy}
            \desc{Confinement energy}{Raises ground state energy}{}
            \desc[german]{Confinement Energie}{Erhöht die Grundzustandsenergie}{}
            \eq{\Delta E = \frac{\hbar^2 \pi^2}{2\masse L^2}}
        \end{formula}

        \Eng[plain_wave]{plain wave}
        \Ger[plain_wave]{ebene Welle}
        \begin{formula}{energy}
            \desc{Energy}{}{}
            \desc[german]{Energie}{}{}
            \eq{E_n = \underbrace{\frac{\hbar^2 k_\parallel^2}{2\masse}}_\text{$x$-$y$: \GT{plain_wave}} + \underbrace{\frac{\hbar^2 \pi^2}{2\masse L^2} n^2}_\text{$z$}}
        \end{formula}

    \Subsection[
        \eng{1D electron gas / quantum wire}
        \ger{1D Eleltronengas / Quantendraht}
        ]{1deg}

        \begin{formula}{energy}
            \desc{Energy}{}{}
            \desc[german]{Energie}{}{}
            \eq{E_n = \frac{\hbar^2 k_x^2}{2\masse} + \frac{\hbar^2 \pi^2}{2\masse L_z^2} n_1^2 + \frac{\hbar^2 \pi^2}{2\masse L_y^2} n_2^2}
        \end{formula}
        
    \Subsection[
        \eng{0D electron gas / quantum dot}
        \ger{0D Elektronengase / Quantenpunkt}
        ]{0deg}

        \TODO{TODO}

\Section[
    \eng{Semiconductors}
    \ger{Halbleiter}
]{semic}
    \begin{formula}{charge_density_eq}
        \desc{Equilibrium charge densitites}{}{}
        \desc[german]{Ladungsträgerdichte im Equilibrium}{}{}
        \eq{
            n_0 &\approx N_\text{c}(T) e^{-\frac{E_\text{c} - \EFermi}{\kB T}} \\
            p_0 &\approx N_\text{v}(T) e^{-\frac{\EFermi - E_\text{v}}{\kB T}} 
        }
    \end{formula}
    \begin{formula}{charge_density_intrinsic}
        \desc{Intrinsic charge density}{}{}
        \desc[german]{Intrinsische Ladungsträgerdichte}{}{}
        \eq{
            n_\text{i} \approx \sqrt{n_0 p_0} = \sqrt{N_\text{c}(T) N_\text{v}(T)} e^{-\frac{E_\text{gap}}{2\kB T}}
        }
    \end{formula}

\Section[
    \eng{Measurement techniques}
    \ger{Messtechniken}
]{meas}
    \Subsection[
        \eng{ARPES}
        \ger{ARPES}
        ]{arpes}
        what?
        in?
        how?
        plot

    \Subsection[
        \eng{Scanning probe microscopy SPM}
        \ger{Rastersondenmikroskopie (SPM)}
        ]{spm}
        \begin{ttext}
            \eng{Images of surfaces are taken by scanning the specimen with a physical probe.}
            \ger{Bilder der Oberfläche einer Probe werden erstellt, indem die Probe mit einer Sonde abgetastet wird.}
        \end{ttext}

        \Eng[name]{Name}
        \Ger[name]{Name}
        \Eng[application]{Application}
        \Ger[application]{Anwendung}


        \begin{minipagetable}{amf}
            \entry{name}{
                \eng{Atomic force microscopy (AMF)}
                \ger{Atomare Rasterkraftmikroskopie (AMF)}
            }
            \entry{application}{
                \eng{Surface stuff}
                \ger{Oberflächenzeug}
            }
            \entry{how}{
                \eng{With needle}
                \ger{Mit Nadel}
            }
        \end{minipagetable}
        \begin{minipage}{0.5\textwidth}
            \begin{figure}[H]
                \centering
                \includegraphics[width=0.8\textwidth]{img/cm_amf.pdf}
                \caption{\cite{Bian2021}}
            \end{figure}
        \end{minipage}


        \begin{minipagetable}{stm}
            \entry{name}{
                \eng{Scanning tunneling microscopy (STM)}
                \ger{Rastertunnelmikroskop (STM)}
            }
            \entry{application}{
                \eng{Surface stuff}
                \ger{Oberflächenzeug}
            }
            \entry{how}{
                \eng{With TUnnel}
                \ger{Mit TUnnel}
            }
        \end{minipagetable}
        \begin{minipage}{0.5\textwidth}
            \begin{figure}[H]
                \centering
                \includegraphics[width=0.8\textwidth]{img/cm_stm.pdf}
                \caption{\cite{Bian2021}}
            \end{figure}
        \end{minipage}

\Section[
    \eng{Fabrication techniques}
    \ger{Herstellungsmethoden}
    ]{fab}
    \begin{minipagetable}{cvd}
        \entry{name}{
            \eng{Chemical vapor deposition (CVD)}
            \ger{Chemische Gasphasenabscheidung (CVD)}
        }
        \entry{how}{
            \eng{
                A substrate is exposed to volatile precursors, which react and/or decompose on the heated substrate surface to produce the desired deposit.
                By-products are removed by gas flow through the chamber.
            }
            \ger{
                An der erhitzten Oberfläche eines Substrates wird aufgrund einer chemischen Reaktion mit einem Gas eine Feststoffkomponente abgeschieden.
                Nebenprodukte werden durch den Gasfluss durch die Kammer entfernt.
            }
        }
        \entry{application}{
            \eng{
                \begin{itemize}
                    \item Polysilicon \ce{Si}
                    \item Silicon dioxide \ce{SiO_2}     
                    \item Graphene
                    \item Diamond
                \end{itemize}
            }
            \ger{
                \begin{itemize}
                    \item Poly-silicon \ce{Si}
                    \item Siliziumdioxid \ce{SiO_2}     
                    \item Graphen
                    \item Diamant
                \end{itemize}
            }
        }
    \end{minipagetable}
    \begin{minipage}{0.5\textwidth}
        \centering
        \includegraphics[width=\textwidth]{img/cm_cvd_english.pdf}
    \end{minipage}


    \Subsection[
        \eng{Epitaxy}
        \ger{Epitaxie}
        ]{epitaxy}
        \begin{ttext}
            \eng{A type of crystal groth in which new layers are formed with well-defined orientations with respect to the crystalline seed layer.}
            \ger{Eine Art des Kristallwachstums, bei der mindestens eine kristallographische Ordnung der wachsenden Schicht der des Substrates entspricht.}
        \end{ttext}

        \begin{minipagetable}{mbe}
            \entry{name}{
                \eng{Molecular Beam Epitaxy (MBE)}
                \ger{Molekularstrahlepitaxie (MBE)}
            } 
            \entry{how}{
                \eng{In a ultra-high vacuum, the elements are heated until they slowly sublime. The gases then condensate on the substrate surface}
                \ger{Die Elemente werden in einem Ultrahochvakuum erhitzt, bis sie langsam sublimieren. Die entstandenen Gase kondensieren dann auf der Oberfläche des Substrats}
            }
            \entry{application}{
                \eng{
                    \begin{itemize}
                        \item Gallium arsenide \ce{GaAs}
                    \end{itemize}
                    \TODO{Link to GaAs}
                }
                \ger{
                    \begin{itemize}
                        \item Galliumarsenid \ce{GaAs}
                    \end{itemize}
                }
            }
        \end{minipagetable}
        \begin{minipage}{0.5\textwidth}
            \centering
            \includegraphics[width=\textwidth]{img/cm_mbe_english.pdf}
        \end{minipage}

