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We obtain exact expressions for the local current and shot noise and thenonlocal shot noise in the first propagating channel of an NSN(normal-superconducting-normal) nanowire. Using high-$T_c$ cupratesuperconductors (HTS) as our model systems we utilize a scattering theoryapproach to derive the scattering matrix for the systems in the hightransparency limit and without the Andreev approximation. The local current andshot noise spectrum is calculated and plotted. In view of recent work in thearea of cooper-pair splitting (CPS) devices, we investigate the nonlocal shotnoise and relate the behavior of the noise as we change parameters such as thesystem size, the orientation of the order parameter and the biasing of thejunction in the HTS NSN system.

Local and Nonlocal Shot Noise in High-$T_C$ Superconducting Nanowires