Modified small-world networks as models of liquid and amorphous selenium

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Abstract
In this work, we present a model of the disordered phases of selenium based upon ideas akin to small-world networks. This model accounts for the description of defect centers of liquid and amorphous Se, which can be introduced in a controllable manner in a broad interval of concentrations. The electronic structure is described by a tight-binding Hamiltonian, which is extended by a Hubbard term to take the influence of an effective electron-electron interaction into account. The resulting electronic structure problem is solved self-consistently. The electronic structure is analyzed in terms of the density of states, the charge order originating from defect states, the charge distribution function, and the localization properties of the eigenfunctions. Only bipolaron states—which compensate the charge of anionic dangling bonds—and positively charged centers with a threefold coordination give rise to impurity states within the band gap of the unperturbed system: The latter species corresponds to one of the defects of the Kastner, Adler, and Fritzsche model of selenium. Within the models studied here, states corresponding to negatively charged singly coordinated atoms lie deep within the bulk of the density of states, and their positively charged counterparts are not observed at all.