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

Abstract

Theories of proximity effect in layered superconductor-normal-metal ͑SN͒ 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, ⌬͑x͒ ϰ / x, as a function of the distance from the SN boundary, x, with a proximity length strongly depending on the repulsive interaction.

Engineering low-temperature proximity effect in clean metals by spectral singularities

“…This statement is valid for distances z smaller than both the thermal decay length ξ T = hv N /kT and the mean-free path l = v N τ , where τ represents the mean time between impurity scattering events [18]. Beyond these distances, the range of the proximity effect will be dictated by the smaller of these two lengths [22][23][24].…”

“…Within the framework of analytical studies and numerical calculations based on the self-consistent Bogoliubov-de Gennes (BdG) equations it was demonstrated that at low (zero) temperatures, the decay of the pair amplitude within the NM deviates from exponential behavior. Instead, the behavior observed in the NM in the ballistic regime follows a power-law decay [9,[15][16][17][18]…”

“…as a function of the distance from the SN interface, z, with a proximity length, ξ. The value of the coefficient α is contingent upon system's dimensionality and can take on different values [9,15,18] 1 2 in 2D, see [19,20] 0 in 1D, see [21] .…”