QUANTUM OSCILLATIONS IN THE ELECTRIC HELD FOR PERPENDICULAR TRANSPORTTHROUGH AN INTERFACE BETWEEN 2 METALLIC LAYERS

We present a quantum statistical theory of the electronic transport th rough an interface between two metallic layers. It is shown that when an electric current flows in the direction perpendicular to the interf aces, spatial oscillations in the charge density and electric field ex ist on both sides of the interface. These oscillations are due to quan tum interference effects between the incident and reflected electrons. They arise when the electrons have different Fermi wave vectors k(F) in the two adjacent metallic layers. The dominant term in these oscill ations has period pi/k(F) and its amplitude decreases as a hyperbolic function of the distance from the interface at short distances (relati ve to the elastic mean-free paths) and exponentially with a characteri stic damping length equal to the mean-free paths at large distances. F urthermore, the presence of a potential barrier of height U at the int erface gives rise to a new interfacial resistance proportional to U-2. For the case of an interface between two ferromagnetic transition met al layers, a discussion of the relative role of s and d electrons in t he in-plane and perpendicular transport is presented.