Phase sensitive electron-phonon coupling in a superconducting proximity structure

We study the role of the superconducting proximity effect on the electron-phonon energy exchange in diffusive normal metals (N) attached to superconductors (S). The proximity effect modifies the spectral response of the normal metal, in particular the local density of states. This leads to a weakening of the electron-phonon energy relaxation. We show that the effect is easily observable with modern thermometry methods, and predict that it can be tuned in structures connected to multiple superconductors by adjusting the phase difference between superconducting order parameters at the two NS interfaces.