Electron cooling by phonons in phase-biased superconducting proximity systems

We investigate the electron-phonon cooling power in disordered electronic systems with a special focus on mesoscopic superconducting proximity structures. Employing the quasiclassical Keldysh Green's function method, we obtain a general expression for the cooling power perturbative in the electron-phonon coupling, but valid for arbitrary electronic systems out of equilibrium. This very general formalism we apply to the case of a disordered superconductor-normal-metal-superconductor proximity structure in equilibrium observing a significantly suppressed cooling power at low temperatures. This effect is related to the existence of a minigap in the quasiparticle spectrum. Furthermore, the minigap is directly controlled by the superconducting phase difference across the junction providing a high tunability of the effect. This makes such structures highly promising candidates for quantum calorimetry.