Electrical properties ofNiS2−xSex

We report results of measurements of electrical conductivity, thermoelectric power, and Hall effect on single crystals of $\mathrm{Ni}{\mathrm{S}}_{2-x}{\mathrm{Se}}_x (0.1\mathrm{}\le x\le 1.5)$. These results cannot be understood using the one-electron approximation but are explained quantitatively by assuming both strong electronic correlations and strong electron-phonon interactions in the $3d e_g$ band associated with the nickel ions. The $\mathrm{Ni}{\mathrm{S}}_{2-x}{\mathrm{Se}}_x$ compounds are of particular interest insofar as they permit study of the effect of increasing bandwidth without a change of the basic occupation of states in the correlation-split $e_g$ bands. In our model, pure stoichiometric $\mathrm{Ni}{\mathrm{S}}_{2-x}{\mathrm{Se}}_x \mathrm{}(x<\mathrm{}0.6\mathrm{})\mathrm{}$ is a Mott insulator with an energy gap due to the correlation splitting of the nickel $e_g$ band. However, in all real samples, nonstoichiometry and/or traces of impurities lead to a small concentration of free carriers at all temperatures. These carriers form small polarons, which ordinarily conduct only by means of thermally activated hopping in a very narrow band. For $0.45\le x<\mathrm{}0.6\mathrm{}$, the conductivity decreases with increasing temperature below about 100 K. We interpret this unusual behavior as due to small-polaron band conduction, a phenomenon predicted by Holstein and others at low temperatures but heretofore unconfirmed. For $x\ge 0.6$, small polarons do not form, and the system is metallic at all temperatures.