diff --git a/Lecture-9-slides-for-printing-slide-8-wave-types.pdf b/Lecture-9-slides-for-printing-slide-8-wave-types.pdf new file mode 100755 index 0000000..81bbc82 Binary files /dev/null and b/Lecture-9-slides-for-printing-slide-8-wave-types.pdf differ diff --git a/Lecture-9-slides-for-printing-slide-8-wave-types.svg b/Lecture-9-slides-for-printing-slide-8-wave-types.svg new file mode 100755 index 0000000..f01a752 --- /dev/null +++ b/Lecture-9-slides-for-printing-slide-8-wave-types.svg @@ -0,0 +1,538 @@ + +image/svg+xml+++––++––i–is-waveBCSp-wave (py)p-wave (px+ ipy)d-waveHigh-TCcuprates diff --git a/references.bib b/references.bib index a32fa26..f17a9c9 100755 --- a/references.bib +++ b/references.bib @@ -121,3 +121,18 @@ Results from previous neutron measurements are found to be consistent with the X author = {Annett, James F.}, year = {2004}, } + +@article{ozcan, + title = {London penetration depth measurements of the heavy-fermion superconductor {CeCoIn} $_{\textrm{5}}$ near a magnetic quantum critical point}, + volume = {62}, + issn = {0295-5075, 1286-4854}, + url = {https://iopscience.iop.org/article/10.1209/epl/i2003-00411-9}, + doi = {10.1209/epl/i2003-00411-9}, + number = {3}, + urldate = {2022-05-18}, + journal = {Europhysics Letters (EPL)}, + author = {Özcan, S and Broun, D. M and Morgan, B and Haselwimmer, R. K. W and Sarrao, J. L and Kamal, Saeid and Bidinosti, C. P and Turner, P. J and Raudsepp, M and Waldram, J. R}, + month = may, + year = {2003}, + pages = {412--418}, +} diff --git a/superconductivity_assignment5_kvkempen.tex b/superconductivity_assignment5_kvkempen.tex index 5e15d16..5f0e843 100755 --- a/superconductivity_assignment5_kvkempen.tex +++ b/superconductivity_assignment5_kvkempen.tex @@ -132,16 +132,37 @@ Conventional superconductors we can describe using BCS theory or some extension 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. +Starting with macroscopic ones, we have the critical temperature $T_c$ and critical field(s) $H_c$. +The microscopic behavior is described by three characteristic lengths\cite[p.62]{annett}: +the coherence length $\xi$ of the Cooper pairs, the penetration depth $\lambda$ of the external field, and the mean free path $\ell$ of the electrons. +These quantities are related to the energy band gap around the Fermi surface in BCS theory. +A nice table summarizing these quantities can be found in \cite[table 10.1, p. 191]{waldram}. 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 +The penetration depth $\lambda$ is determined by the superfluid density $n_s$ in the two fluid model. +As $n_s$ can be related to energy gap $\Delta$\cite[ch. 7]{annett}, so can thus $\lambda$ be. +It is not the maximum value of $\Delta$ we are after, but more its variation in momentum space. +Results on the relation between the nodes of the energy gap and the type of superconducting wave we deal with can be seen in figure \ref{fig:waves}. + +\begin{figure} + \centering + \includegraphics[width=.8\textwidth]{Lecture-9-slides-for-printing-slide-8-wave-types.pdf} + \caption{Different types of superconductor waves have different node patterns. The figure is from the slides of lecture 9 by Alix McCollam.} + \label{fig:waves} +\end{figure} + +In the weak coupling limit of BCS theory, the coherence length can be related to the gap parameter\cite[ch. 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}. +BCS describes s-wave superconductors. +Around the Fermi sphere, we see a constant band gap. +For other types, this is not the case: there is gap anisotropy. +But now the question is how we can measure this gap anisotropy. +A hard requirement, is that the probe should be sensitive to the direction of the electron momenta\cite[p.207]{waldram}, for which there are multiple methods. +We will focus on using $\lambda(T)$ measurements using tunnel diode oscillators (TDO)\cite{ozcan}, as that technique is used in the provided paper. \bibliographystyle{vancouver} \bibliography{references.bib}