Mobility edge and AC conductivity for quasi-two-dimensional weakly disordered system

For highly anisotropic layered material the influence of weak disorder due to randomly distributed impurities is studied in diagrammatic self-consistent approximation. It is shown that, in contrast to a quasi-one-dimensional case, extended states in an upper part of an energy band immediately appear if a weak interlayer tunnelling is switched on. Intensity of this tunnelling is characterised by the value of interplane exchange integral omega . The borderline energy between extended and localised states is equal to epsilon c =(h(cross)/ pi tau )ln( square root 2h(cross)/ omega tau ), where tau is the intralayer relaxation time. For epsilon F < epsilon c system behaves as a dielectric and for epsilon F > epsilon c it behaves as a metal. Here epsilon F is the Fermi energy. AC conductivity sigma ( omega ) is found for both cases. The localisation length is calculated for epsilon F <or= epsilon c .