Spin dependent Andreev refelction What happens with the spin in Andreev reflection process ? The simple Bogoliubov - De Gennes equation for hole and electron does not contain information about the spin. I know there are some generalizations to spin dependent formalism but I can't find good refrence. Can You recommend good papers/books about spin dependent scattering processes - spin dependent Andreev reflection (when it changes or not); spin physics in proximity of superconductor.
 A: The BdG equation reads, in full spin-space, and for a s-wave superconductors
$$\left(\begin{array}{cccc}
H_{0}\left(p\right) & 0 & 0 & \Delta\\
0 & H_{0}\left(p\right) & -\Delta & 0\\
0 & \Delta^{\ast} & -H_{0}^{\ast}\left(-p\right) & 0\\
-\Delta^{\ast} & 0 & 0 & -H_{0}^{\ast}\left(-p\right)
\end{array}\right)\left(\begin{array}{c}
u_{\uparrow}\left(p\right)\\
u_{\downarrow}\left(p\right)\\
v_{\uparrow}\left(-p\right)\\
v_{\downarrow}\left(-p\right)
\end{array}\right)=\varepsilon\left(\begin{array}{c}
u_{\uparrow}\left(p\right)\\
u_{\downarrow}\left(p\right)\\
v_{\uparrow}\left(-p\right)\\
v_{\downarrow}\left(-p\right)
\end{array}\right)$$
so it is quite often (always ?) decoupled as you most probably seen it in two spin sectors
$$\left(\begin{array}{cc}
H_{0}\left(p\right) & \Delta\\
-\Delta^{\ast} & -H_{0}^{\ast}\left(-p\right)
\end{array}\right)\left(\begin{array}{c}
u_{\uparrow}\\
v_{\downarrow}
\end{array}\right)=\varepsilon\left(\begin{array}{c}
u_{\uparrow}\\
v_{\downarrow}
\end{array}\right)$$
and $$\left(\begin{array}{cc}
H_{0}\left(p\right) & -\Delta\\
\Delta^{\ast} & -H_{0}^{\ast}\left(-p\right)
\end{array}\right)\left(\begin{array}{c}
u_{\downarrow}\\
v_{\uparrow}
\end{array}\right)=\varepsilon\left(\begin{array}{c}
u_{\downarrow}\\
v_{\uparrow}
\end{array}\right)$$
and we verify the usual dispersion $\varepsilon^{2}=H_{0}^{2}+\left|\Delta\right|^{2}$ when $H_{0}^{\ast}\left(-p\right)=H_{0}\left(p\right)$.
Now for a free-electron gas with BCS-paring, one has $H_{0}\left(p\right)=p^{2}/2m-\mu\approx v_{F}\left(p-p_{F}\right)$ and the Andreev reflexion of a spin-up electron at wave-vector $+k$ is a spin-down hole at wave-vector $-k$ at a N/S interface. So at the interface there is neither momentum ($+k+(-k)=0$), nor spin ($\uparrow +\downarrow = 0$) accumulation. There is nevertheless a charge accumulation ($-e-(+e)=-2e$, aha ! the charge of a Cooper pair !), see the seminal paper by Tinkham, Blonder and Klapwijk (actually, Klapwijk is still working (well, I've seen a paper from his group this week on the arXiv), so contact him to see his paper if you have trouble with the pay-wall, he's at TU-Delft, the Netherlands).
The reason why no-one discusses spin-problem with s-wave superconductor is because of the singlet pairing, so there is no spin-accumulation at the S/N interface.
Spin-problem in proximity with superconductors have a few reviews: 

A.I. Buzdin, RMP 77 935 (2005) arXiv:cond-mat/0505583
F. S. Bergeret,  A. F. Volkov, K. B. Efetov, RMP 77 1321 (2005) arXiv:cond-mat/0506047

well, spin here means ferromagnet (generically called S/F proximity effects), but the topic is pretty broad now, so precise your question after looking at these papers. You can try also the keywords spintronic and superconductivity, you may find some things interesting for you.
I remember I pretty liked a book by Ketterson and Song, Cambridge University Press, (well, a fully inspired name:) Superconductivity (tadam !). They review the BdG formalism for (all?, I don't remember, sorry) coupling in a superconductor. 
