ass1: Elaborate on difference type-I and type-II

superconductivity_assignment1_kvkempen.tex

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 %\usepackage[nottoc,numbib]{tocbibind}
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-\usepackage{svg}
 
 \title{Superconductivity - Assignment 1}
 \author{
@@ -114,13 +113,49 @@ No idea yet.
 \section{Difference between type-I and type-II superconductors}
 In the realm of conventional superconductors, we have type-I and type-II superconductors.
 Both types are mediated by electron-phonon coupling, but there are quite some differences.
+Using figure \ref{fig:typevs}, we will go through their differences.
 
 \begin{figure}
-	\label{fig:type-i-vs-ii}
+	\label{fig:typevs}
-	\includesvg[width=\textwidth]{Lecture-2-slides-for-printing-type-i-vs-ii.svg}
+	\includegraphics[width=\textwidth]{Lecture-2-slides-for-printing-type-i-vs-ii.pdf}
 	\caption{Figure is borrowed from the presentation of week two of the Superconductivity course by Alix McCollam.}
 \end{figure}
 
+Type-I superconductors (sc) are described by BCS theory.
+An example of a type-I sc is lead (Pb).
+Below a critical temperature $T_c$, these materials exhibit perfect diamagnetism.
+Inside the sc, a magnetic field is generated to expell the externally applied field,
+such that the net field is zero.
+This is called the Meissner effect.
+The perfect diamagnetism is quantized as having susceptibility $\chi = -1$.
+There is, however, a limit to how large a field can be completely expelled.
+This is called the critical field $B_c$.
+If $B_c$ is exceeded, the superconductivity breaks down, thus the material will cease to expell the field,
+the diagmagnetism drops to $\chi = 0$.
+This effect is seen in the bottom-left plot in figure \ref{fig:typevs}.
+The relation between these two critical values is given as
+\[
+	B_c(T) = B_c(0) \left[ 1 - \frac{T}{T_c}^2 \right].
+\]
+An example of this curve is plotted in the top-left of figure \ref{fig:typevs}.
+Two phases can be distinguished:
+the Meissner (or superconducting) state under the graph,
+and the normal state outside it.
+The transition between these states is a first-order phase transition due to the discontinuity in the magnetization $M = \frac{dF}{dB}$, the first derivative of the free energy to the applied field.
+
+Then there are type-II sc, for example, niobium (Nb).
+Instead of only having a Meissner or sc phase, they have another phase:
+the vortex state.
+Below $T_c$ and lower critical field $B_{c1}(T)$, the type-II sc is in the Meissner state,
+and the material thus completely cancels the externally applied field.
+Above the upper critical field $B_{c2}(T)$, the material is in the normal state.
+When the field is between these two critical fields, $B_{c1}(T) < B < B_{c2}(T)$,
+the material is in the vortex state.
+In the vortex state, the externally applied magnetic field is not completely expelled.
+Instead, the material consists of normal and sc regions, the former called vortices.
+These vortices are normal conducting regions and allow magnetic flux to pass.
+
+
 Type-I superconductors are thought to be described by BCS theory.
 They are phonon-mediated.
 They have different phase diagrams from type-II superconductors,

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