Urbach Law and Lifshitz Singularity in Spectra of Localized States of Disordered Systems

The density of localized states within the energy interval ranging from the mobility threshold up to the Lifshitz border is found in an instantaneous approach with exponetial accuracy for the three‐dimensional two‐component random system described by single‐band Hamiltonian taking into account diagonal disorder. It is shown that just below the mobility threshold an energy region is placed where the density of states dependence is obeying the Urbach law. Exact and approximate expressions for the Urbach parameter are obtained. Its dependence on the model parameters and the estimation of the absolute value show that the experimental data can be accounted for many disordered systems at reasonable parameters of the Hamiltonian. Arguments are presented speaking in behalf of the existence of an Urbach law in one. and two‐dimensional disordered systems.