Ab initio transport calculations: from normal to superconducting current

Applying the Bogoliubov-de Gennes equations with density-functional theory, it is possible to formulate first-principles description of current-phase relationships in superconducting/normal (magnetic)/superconducting trilayers. Such structures are the basis for the superconducting analog of Magnetoresistive random access memory devices (JMRAM). In a recent paper [1] we presented results from the first attempt to formulate such a theory, applied to the Nb/Ni/Nb trilayers. In the present work we provide computational details, explaining how to construct key ingredient (scattering matrices $S_N$) in a framework of linear muffin-tin orbitals (LMTO).