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

Belzig, W. and Bruder, C. and Fauchere, A. L.. (1998) Diamagnetic response of a normal-metal-superconductor proximity system at arbitrary impurity concentration. Physical Review B, Vol. 58, H. 21. pp. 14531-14540.

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Official URL: http://edoc.unibas.ch/dok/A5252857

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 Greens 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.