  The theoretical description of modern nanoelectronic devices requires a
quantum mechanical treatment and often involves disorder, e.g. form alloys.
Therefore, the ab initio theory of transport using non-equilibrium Green's
functions is extended to the case of disorder described by the coherent
potential approximation. This requires the calculation of non-equilibrium
vertex corrections. We implement the vertex corrections in a
Korringa-Kohn-Rostoker multiple scattering scheme. In order to verify our
implementation and to demonstrate the accuracy and applicability we investigate
a system of an iron-cobalt alloy layer embedded in copper. The results obtained
with the coherent potential approximation are compared to supercell
calculations. It turns out that vertex corrections play an important role for
this system.
