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

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 regime`s 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.