Conductivities and transmission coefficients of ultra-thin disordered metallic films

The diffusive motion of quasi-two-dimensional electron gas through an ultra-thin system of disordered potentials is considered. In such a system, the Fermi sphere splits into a set of independent sheets due to a small thickness of the system. Each sheet can be seen as an electron subband. Electron transport goes through these subbands independently. The sum of electrical conductivities over the subbands determines the total current, which is calculated for ultra-thin films of cesium. We also present the relation between our approach and the Landauer formalism based on the notion of the transmission coefficient.