ass5: Introduce steps we'll take for 17

references.bib

@@ -108,3 +108,16 @@ Staging is observed for all four samples at low temperatures with X-ray measurem
 The temperature dependent phase transitions for both the Bmab structure and the staging reflections are investigated between 5 and 300 K. The critical exponents for the Bmab reflections are found to be significantly lower than results from similar materials in literature, although with transition temperatures consistent with literature for comparable sample compositions. It is found that the critical exponents for the staging reflections increase for increasing doping while the transition temperatures decrease, both consistent with results on the isostructural La2NiO4+y.
 
 Results from previous neutron measurements are found to be consistent with the X-ray measurements in this work, and measured reciprocal space maps from this work show a large variety of other superstructure reflections which will be interesting to investigate in the future.}, publisher={figshare}, author={Ray, Pia Jensen}, year={2016}, month={Feb} } 
+
+@book{annett,
+	edition = {1},
+	series = {{OXFORD} {MASTER} {SERIES} {IN} {CONDENSED} {MATTER} {PHYSICS}},
+	title = {Superconductivity, {Superfluids}, and {Condensates}},
+	volume = {5},
+	isbn = {978-0-19-850756-7 0-19-850756-9},
+	url = {http://physics.ut.ac.ir/~zadeh/teachings/Adv_Super/SC_Annett.pdf},
+	language = {English},
+	publisher = {Oxford University Press},
+	author = {Annett, James F.},
+	year = {2004},
+}

superconductivity_assignment5_kvkempen.tex

@@ -49,6 +49,21 @@
 \begin{document}
 
 \section{$T_c$ upper limit in BCS}
+In BCS theory, the formation of Cooper pairs is mediated by phonons.
+There is a phonon-electron interaction quantified by the dimensionless quantity 
+\[
+	\lambda := Vg(\epsilon_F)
+\]
+with $V$ Cooper's approximate potential and $g(\epsilon_F)$ the density of states near the Fermi surface for the electrons.
+A thorough discussion can be found in Annett's book \cite[chapter 6]{annett} and in the slides of week 6 of this course.
+The binding energy of the Cooper pairs (i.e. the energy gain of forming these pairs) is
+\[
+	-E = 2\hbar\omega_De^{-1/\lambda}.
+\]
+In the weak coupling limit of the BCS theory, the case we have considered so far, it is assumed that $\lambda << 1$.
+It is when this assumption breaks down, BCS does not work and we find an upper limit to the critical temperature $T_c$.
+We will look at a way to express the critical temperature in terms we can derive, and than look at the values that maximize this critical temperature whilst still following BCS theory.
+
 
 \section{Energy gap $\Delta$ et al.}