Localized States in Disordered Lattices

Abstract

Abstract This paper investigates the conditions under which localized states occur in three dimensional disordered systems, and considers the relevance of a large body of experimental data on liquids which exhibit non‐metallic behaviour in their conductivities. It is suggested that in many liquids a “pseudogap” a deep minimum in the density of states will occur. It is argued that localized states will appear in this pseudogap when the density of states drops to roughly half its free electron value and that the mean free path is then approximately equal to the wavelength of the electron. It then follows that “hopping” conductivity increasing with increasing temperature will appear when the magnitude of the conductivity falls below a certain value, computed to be in the neighbourhood of 300 Ω −1 cm −1 . An examination of the known data on about 90 liquids near their melting point suggests that this is in fact the case.