Conduction eigenchannels of atomic-sized contacts: Ab initio KKR Green's function formalism

We develop a formalism for the evaluation of conduction eigenchannels of atomic-sized contacts from first-principles. The multiple scattering Korringa-Kohn-Rostoker (KKR) Green's function method is combined with the Kubo linear response theory. Solutions of the eigenvalue problem for the transmission matrix are proven to be identical to eigenchannels introduced by Landauer and B{\"u}ttiker. Applications of the method are presented by studying ballistic electron transport through Cu, Pd, Ni and Co single-atom contacts. We show in detail how the eigenchannels are classified in terms of irreducible representations of the symmetry group of the system as well as by orbital contributions when the channels wave functions are projected on the contact atom.