Coulomb versus Madelung Gap: Ordering in a System of Point Charges

Spatial correlations of impurity charges in a mixed valence regime are studied with the use of Monte Carlo simulations. The influence of various kinds of disorder on the one-particle density of states is determined. A continuous transitions from a "soft" Coulomb gap (density of states vanishing only at the chemical potential) to a "hard" gap (with a finite range of energies with vanishing density of states) is found, driven by decreasing amount of built-in disorder in the system. The "hard" Coulomb gap resembles the Madelung gap, found in crystalline arrangements of charges. The similarity reflects the fact that both the Coulomb and Madelung gaps are manifestations of the same phenomenon, resulting from ordering of the positions of point charges, the only difference being the range of correlations.