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I know that inverse proximity effect affect the order parameter of the superconductor and that triplet proximity effect convert singlet Cooper pairs into triplets. But how is the two phenomena connected? And what is their relevance when it comes to Andreev reflections?

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typically the superconducting proximity effect denotes the leaking of the superconducting features in a non-superconducting metal which is put in good electric contact with a superconductor. As you correctly stated, there is also an inverse effect, namely that the superconducting order parameter is reduced as well. Note that, in general, the size of these two effects strongly depends on the geometrical dimensions of the superconducting and the non-superconducting elements, and on how they compare.

In this optic, something interesting happens when you put a superconductor in close contact with a ferromagnetic element. In particular, among them, there is the possibility of the generation of spin-triplet supercurrents. I am not an expert on that, so I suggest you two excellent reviews on these topics.

https://www.nature.com/articles/nphys3242

https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.77.1321

Please ask if something is not clear to you.

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