The density of states in the Coulomb gap

Abstract

Abstract A new bound on the density of single-particle states N 1(E) in the Coulomb gap is derived. This is exponential in three-dimensional systems, A(E/E 0)−3/2 × exp{-(E/E 0)−1)}, and a power-law in two dimensions. The method, following the suggestion of Efros and Shklovskii (1975), is to consider the relaxation around a particle added to the ground state. The electric field of this extra charge induces electron-hole transitions in the surroundings, which lower the total energy of the excitation. The energy must not become negative, however; so the distribution of relaxation energies, which I have calculated using Chandraskehar's method, provides a bound on N 1(E). The calculation also shows how the Coulomb gap for ‘electronic polarons’ narrows rapidly as the region of relaxation included in the excitation increases.