Minor patches.

chapters/appendices/derivations.tex

@@ -25,7 +25,7 @@ \section{Phase-flux relation}
 \end{align}
 Substituting $\vec{v}$ with a more useable expression in terms of the current density $\vec{J}$ and $\lambda$ using Equation~\ref{eqn:london-penetration-depth}.
 \begin{align}
-	\vec{J} = -2e|\psi|^2\vec{v} = -\frac{m_e}{\lambda^2e\mu_0}\vec{v} \Rightarrow \vec{v} = -\frac{\lambda^2e\mu_0}{m_e}\vec{J}
+	\vec{J} = -2e|\Psi|^2\vec{v} = -\frac{m_e}{\lambda^2e\mu_0}\vec{v} \Rightarrow \vec{v} = -\frac{\lambda^2e\mu_0}{m_e}\vec{J}
 \end{align}
 Combining the two equations gives us a useable expression for $\vec{A}$ in the loop:
 \begin{align}

chapters/introduction/main.tex

@@ -1,9 +1,9 @@
 % !TEX root = ../../thesis.tex
 \chapter{Introduction}
-Josephson junctions have a wide variety of applications. Notable applications are qubits\cite{placeNewMaterialPlatform2021,pechenezhskiySuperconductingQuasichargeQubit2020}, dissipationless electronics through Josephson diodes\cite{zhangReconfigurableMagneticfieldfreeSuperconducting2023a,ciacciaGateTunableJosephson2023} and microscopic imaging techniques\cite{clarkeSQUIDHandbook2004,rogSQUIDontipMagneticMicroscopy2022,pranceSensitivityDCSQUID2023}. The behaviour of a Josephson junctions is governed by their current-phase relation (CPR). Probing the CPR can lead to new insights and applications. By measuring the CPR it is possible to if the junction's behaviour is ballistic or diffusive\cite{endresCurrentPhaseRelation2023,kayyalhaHighlySkewedCurrent2020}. Additionally, it has proven the existence of $0$-$\pi$ and $\varphi_0$ junctions\cite{frolovMeasurementCurrentPhaseRelation2004,muraniBallisticEdgeStates2017} as well as non-$2\pi$ periodic CPRs\cite{endresCurrentPhaseRelation2023}.
+Josephson junctions have a wide variety of applications. Notable applications are qubits\cite{placeNewMaterialPlatform2021,pechenezhskiySuperconductingQuasichargeQubit2020}, dissipationless electronics through Josephson diodes\cite{zhangReconfigurableMagneticfieldfreeSuperconducting2023a,ciacciaGateTunableJosephson2023} and microscopic imaging techniques\cite{clarkeSQUIDHandbook2004,rogSQUIDontipMagneticMicroscopy2022,pranceSensitivityDCSQUID2023}. The behaviour of a Josephson junctions is governed by their current-phase relation (CPR). Probing the CPR can lead to new insights and applications. By measuring the CPR it is possible to if the junction's behaviour is ballistic or diffusive\cite{endresCurrentPhaseRelation2023,kayyalhaHighlySkewedCurrent2020}. Additionally, it has proven the existence of $0$-$\pi$ and $\varphi_0$ junctions\cite{frolovMeasurementCurrentPhaseRelation2004,muraniBallisticEdgeStates2017,strambiniJosephsonPhaseBattery2020,szombatiJosephsonPh0junctionNanowire2016} as well as non-$2\pi$ periodic CPRs\cite{endresCurrentPhaseRelation2023}.
 
 In our group there is an interest in the CPR of rings of \ce{Sr2RuO4}. Recent work by Lahabi \textit{et al.} provides evidence for the existence of chiral domain walls in homogenous rings of \ce{Sr2RuO4}\cite{lahabiSpintripletSupercurrentsOdd2018} that act as Josephson junctions. As such \ce{Sr2RuO4} rings show dc-SQUID like behaviour without the presence of constrictions, grain boundaries or an interface with a different material. More definitive proof for chiral domain walls could be found by measuring the Josephson energy\cite{lahabiSpintripletSupercurrentsOdd2018,sigristRoleDomainWalls1999}. The most elegant way to determine the Josephson energy is to measure the CPR.
 
-This thesis utilizes a method based on the work of Frolov \textit{et al.}. The reader is referred to \cite{frolovMeasurementCurrentPhaseRelation2004,frolovCurrentphaseRelationsJosephson2005} for their work. We explore a method to measure the current-phase relation of a single Josephson junction which, if successful, can be extended in later studies to measure the current-phase relation of \ce{Sr2RuO4} rings.
+This thesis utilizes a method based on the work of Frolov \textit{et al.}. The reader is referred to~\cite{frolovMeasurementCurrentPhaseRelation2004,frolovCurrentphaseRelationsJosephson2005} for their work. We explore a method to measure the current-phase relation of a single Josephson junction which, if successful, can be extended in later studies to measure the current-phase relation of \ce{Sr2RuO4} rings.
 
 The next chapter will lay a theoretical foundation for our method. Chapter~\ref{chapter:method} delves deeper into the method and presents numerical calculations to guide our expectations. Then our results are presented on a per sample. Finally a conclusion is drawn and we sketch an outlook for future research.

chapters/samples/main.tex

@@ -5,11 +5,14 @@ \chapter{Samples}
 \section{Sample CP1.2H}
 \input{chapters/samples/CP1.2H/main}
 
+\newpage
 \section{Sample CP2.6B}
 \input{chapters/samples/CP2.6B/main}
 
+\newpage
 \section{Sample CP3.5A}
 \input{chapters/samples/CP3.5A/main}
 
+\newpage
 \section{Sample CP2.6B revisited}
 \input{chapters/samples/CP2.6B_revisited/main}

chapters/theory/main.tex

@@ -12,7 +12,7 @@ \section{Superconductors}
 \end{equation}
 Both $\left|\Psi\right|$ and $\varphi$ are functions of position. The behaviour of this wave function is described by the Ginzburg-Landau theory. In this theory, $|\Psi|^2$ is a measure for the density of Cooper pairs (units of \unit{\per\cubic\meter}). The super current density (\unit{\ampere\per\square\meter}) is given by\footnote{See \citetitle{tinkhamIntroductionSuperconductivity} equation 4.14a.}:
 \begin{equation}
-	\vec{J_s} = e^* |\psi|^2 \vec{v_s} = \frac{e^*}{m^*} |\psi|^2 \left(\hbar \nabla \varphi-\frac{e^*}{c} \vec{A}\right) \stackrel{\text{SI}}{=} \frac{e}{m_e} |\psi|^2 \left(\hbar \nabla \varphi + 2e \vec{A}\right)
+	\vec{J_s} = e^* |\Psi|^2 \vec{v_s} = \frac{e^*}{m^*} |\Psi|^2 \left(\hbar \nabla \varphi-\frac{e^*}{c} \vec{A}\right) \stackrel{\text{SI}}{=} \frac{e}{m_e} |\Psi|^2 \left(\hbar \nabla \varphi + 2e \vec{A}\right)
 	\label{eqn:super-current}
 \end{equation}
 
@@ -32,7 +32,7 @@ \subsection{Characteristic length scales}
 
 The second length scale is the penetration depth $\lambda$. It is a measure for the `stiffness' of the phase. A small $\lambda$ means $\varphi$ can change easily. This means larger super currents are possible. The currents can screen magnetic fields which penetrate roughly on the same length scale. The penetration depth in Ginzburg-Landau theory at \qty{0}{\kelvin} is given by\footnote{See \citetitle{tinkhamIntroductionSuperconductivity} equation 4.8.}:
 \begin{align}
-	\lambda(0) &= \sqrt{\frac{m^*c^2}{4\pi|\psi|^2e^{*2}}} \stackrel{\text{SI}}{=} \sqrt{\frac{m_e}{2|\psi|^2e^2\mu_0}}
+	\lambda(0) &= \sqrt{\frac{m^*c^2}{4\pi|\Psi|^2e^{*2}}} \stackrel{\text{SI}}{=} \sqrt{\frac{m_e}{2|\Psi|^2e^2\mu_0}}
 	\label{eqn:london-penetration-depth}
 \end{align}
 The penetration depth too is dependent on temperature and decreases for higher temperatures. For more information on length scales the reader is referred to \citetitle{tinkhamIntroductionSuperconductivity} by \citeauthor{tinkhamIntroductionSuperconductivity}.
@@ -102,7 +102,7 @@ \section{dc-SQUID magnetometers}
 	\label{fig:schematic-dc-SQUID}
 \end{figure}
 
-This behaviour gives rise to the `dc-SQUID interference pattern' (SQI). Such a pattern is shown in Figure~\ref{example-SQI}. Most importantly, this pattern is exactly $\Phi_0$ periodic independent of any device geometries. As such it is very easy to calibrate. Two parameters are important for the sensitivity and hysteresis\cite{clarkeSQUIDHandbook2004}:
+This behaviour gives rise to the `dc-SQUID interference pattern' (SQI). Such a pattern is shown in Figure~\ref{fig:example-SQI}. Most importantly, this pattern is exactly $\Phi_0$ periodic independent of any device geometries. As such it is very easy to calibrate. Two parameters are important for the sensitivity and hysteresis\cite{clarkeSQUIDHandbook2004}:
 \begin{equation}
 	\beta_c = \frac{2\pi}{\Phi_0}I_cR^2C
 	\tag{Stewart-McCumber parameter}

preamble.tex

@@ -8,7 +8,7 @@
 
 % Use siunitx to write out units and quantities, use special formatting for the units.
 \usepackage{siunitx}
-\sisetup{separate-uncertainty = true, multi-part-units = single, inter-unit-product = \ensuremath { { } \cdot { } }, range-units = single, list-units = single}
+\sisetup{separate-uncertainty = true, multi-part-units = single, inter-unit-product = \ensuremath { { } \cdot { } }, range-units = single, list-units = single, exponent-product=\cdot}
 \DeclareSIUnit\fluxquantum{\text{\ensuremath{\Phi_0}}}
 
 % Setup bibliography (instead of relying on the way lion-msc does it using natbib).