Diamagnetic response of a normal-metal–superconductor proximity system at arbitrary impurity concentration

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Abstract
We investigate the magnetic response of normal-metal–superconductor proximity systems for arbitrary concentrations of impurities and at arbitrary temperatures. Using the quasiclassical theory of superconductivity a general linear-response formula is derived which yields a nonlocal current-field relation in terms of the zero-field Green’s functions. Various regimes between clean-limit and dirty-limit response are investigated by analytical methods and by solving the general formula numerically. In the ballistic regime, a finite mean free path reduces the nonlocality and leads to a stronger screening than in the clean limit even for a mean free path much larger than the system size. Additionally, the range of the kernel describing the nonlocality is strongly temperature dependent in this case. In the diffusive limit we find a crossover from local to nonlocal screening, which restricts the applicability of the dirty-limit theory.