Low-temperature proximity effect in clean metals with repulsive electron-electron interaction

Theories of proximity effect in layered superconductor–normal-metal SN structures usually deal with a hypothetic normal metal with no direct repulsive interaction between electrons and with finite temperatures often close to the superconductor critical temperature. We present an asymptotic solution of the Gor’kov equations in the opposite low-temperature limit for a clean normal metal with a repulsive interaction between electrons. The order parameter in the metal exhibits a power-law decay, x /x, as a function of the distance from the SN boundary, x, with a proximity length strongly depending on the repulsive interaction.