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, $\Delta \left(x\right)\propto \xi /x$, as a function of the distance from the SN boundary, $x$, with a proximity length $\xi$ strongly depending on the repulsive interaction.

Figure 1

(Color online) The order-parameter profile near the boundary between a superconductor (S) and a normal metal (N) with the repulsive electron-electron interaction.

Figure 2

(Color online) Four domains with different solutions for GFs with the steplike order parameter $\Delta \left(x\right)={\Delta }_s\Theta \left(-x\right)$.

Figure 3

SN proximity length $\xi$ (in units of the superconductor coherence length) as a function of the repulsive pseudopotential ${\mu }_c$ (solid line) and of the attractive potential (dashed line).