QUANTUM OSCILLATIONS IN THE ELECTRIC FIELD FOR PERPENDICULAR TRANSPORT THROUGH AN INTERFACE BETWEEN 2 METALLIC LAYERS

We present a quantum statistical theory of the electronic transport through an interface between two metallic layers. It is shown that when an electric current flows in the direction perpendicular to the interfaces, spatial oscillations in the charge density and electric field exist on both sides of the interface. These oscillations are due to quantum 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 oscillations has period pi/k(F) and its amplitude decreases as a hyperbolic function of the distance from the interface at short distances (relative to the elastic mean-free paths) and exponentially with a characteristic damping length equal to the mean-free paths at large distances. Furthermore, the presence of a potential barrier of height U at the interface gives rise to a new interfacial resistance proportional to U-2. For the case of an interface between two ferromagnetic transition metal layers, a discussion of the relative role of s and d electrons in the in-plane and perpendicular transport is presented.