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An S-N-S Josephson junction is formed by two Superconducting (S) leads separated by a normal metal (N) which acts like the weak link. While studying, I often encounter the words diffusive, long, short, in clean limit and dirty limit. I see that they describe the different regimes of the SNS Junction.

I am trying to establish a global understanding of these regimes based on the characteristic lengths existing on an SNS junction. Namely,

L: Length of the normal metal

$\textbf{$L_b$ $\sim$ $\frac{\hbar V_F}{\Delta}$} :$ Coherence length (based on the answer)

$\textbf{$L_\Phi$ $\sim$ $\sqrt{\frac{\hbar D}{\Delta}}$} $ : Coherence length in diffusive regime

$\textbf{$L_{th}$ $\sim$ $\sqrt{\frac{\hbar D}{ k_b T}}$} $ : Thermal length in diffusive regime (2)

Also,

$\epsilon_c = \frac{\hbar D}{L^²}$ : Thouless energy

According to this article, the characteristic voltage, $\textbf{$V_c = R_N I_c$}$, is governed by $\epsilon_{c}$ or the gap $\Delta$. (whichever is smaller)

In light of these informations;

  • Would it be correct to construct a table such as below ?

$$\begin{array}{|c|c|c|} \hline &\textbf{Long}&\textbf{Short}\\ \hline \textbf{Diffusive} \\ \textit{(dirty limit)}&L >> L_{\phi}, (\epsilon_c << \Delta) &L << L_{\phi}, (\epsilon_c >> \Delta)\\ \hline \\ \textbf{Ballistic} \\ \textit{(clean limit)} &L >> L_{b}&L << L_{b}\\ \hline \hline \end{array}$$

  • I can't see where $L_{th}$ fits in this picture. When and how does it become an important length scale ?

Thanks

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