Conductivity 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 system the Fermi sphere splits into a set of independent sheets due to the small thickness of the system. Each sheet can be seen as an electron sub-band. The electron transport goes through these sub-bands independently. The sum of electrical conductivities over these sub-bands determines the total current which is calculated for ultra-thin films of cesium. We also present the relation between our approach and Landauer formalism based on the notation of the transmission coefficient.