ass5: Draft essay 18

superconductivity_assignment5_kvkempen.tex

@@ -124,8 +124,23 @@ This leads to our final maximum
 For larger $T_c$ values, larger binding of Cooper pairs would be needed to overcome the thermal energy.
 This means our assumption of weak coupling breaks down, making most of the derivation invalid without further arguments.
 
-\section{Energy gap $\Delta$ et al.}
+\clearpage
 
+\section{Penetration depth $\lambda$ and measuring it}
+There are many species of superconductors.
+Conventional superconductors we can describe using BCS theory or some extension of it.
+Others we do not yet have a theory for.
+Some are type-I, others type-II.
+What they do have in common, is that they can be characterized by some key quantities.
+Starting with the coherence length $\xi$ and the penetration depth $ \lambda$, we also have their critical temperatures $T_c$ and can relate them to the energy band gap around the Fermi surface in BCS theory.
+In this essay, we will take a look at what the penetration depth can tell us about the superconducting energy gap, and will go into measuring the penetration depth.
+
+In the weak coupling limit of BCS theory, the coherence length can be related to the gap parameter\cite[chapter 9]{waldram} as
+\[
+	\xi_{BCS} = \frac{\hbar v_F}{\pi\Delta},
+\]
+for $v_F$ the Fermi velocity.
+Furthermore, it has the physical interpretation of the size of the separation in a Cooper pair\cite[p. 62]{annett}.
 
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