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

The present study investigates the behavior of the Cooper pair wave function in a normal metal (NM) near superconductor-NM-junctions, specifically focusing on the ballistic regime at zero temperature. It is widely assumed that the wave function follows a power-law decay, with the decay exponents dependent on the system's dimensionality. Our work reveals that the multiband nature of a compound significantly influences the damping degree of pair amplitudes in an NM, rendering it sensitive to the position of the Fermi level. To explore this phenomenon, we employ the numerical method of self-consistent Bogoliubov-de Gennes equations, utilizing a nanowire as a model for an electronic multiband system. By analyzing the obtained pair amplitudes, we extract relevant lengths and exponents that characterize the leakage of superconducting correlations. We further examine this phenomenon by varying the sample's cross-sectional size and the superconducting coupling constant. Consequently, our findings demonstrate that the properties of a superconducting/NM junction's proximity effect can be manipulated not only through temperature, total impurity and defect density, but also by controlling the position of the Fermi level. This tunability enables the transition from a long-range regime to a short-range one, providing valuable insights for designing and understanding such junctions in practical applications.