Coulomb gaps and Hubbard gaps

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Abstract
There is a strong unscreened Coulomb repulsion between the electrons in the impurity band of a lightly doped compensated semiconductor. This can be divided into a long-ranged 1/r part and a short-ranged part between two electrons on the same site. Both of these interactions may lead to gaps in the density of single-particle states, the Coulomb gap and the Hubbard gap respectively. The properties of these two types of gap are explored in this paper using a classical model of an impurity band. The model was originally used by Efros and Shklovskii (1975) to study the Coulomb gap for spinless electrons. Including spin and the Hubbard (on-site) interaction leads to some interesting changes in the form of the Coulomb gap. Under the conditions appropriate for the impurity band of a lightly doped crystalline semiconductor the gap is asymmetric and in most situations the coefficient of the parabolic dip in the density of states is different from that calculated by Efros. The case of a negative Hubbard U, as may be relevant for a non-crystalline semiconductor, is also discussed briefly.

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