On the electronic structure of an impurity band: a cumulant approach

The electronic structure of an impurity band in a heavily-doped semiconductor, in the metallic regime just above the Mott transition, is studied in a tight-binding scheme using a cumulant expansion. The density of states shows no erosion in its centre near the impurity level; a result confirmed by a detailed comparison between results obtained either by a numerical simulation technique or by other analytical approaches. This comparison also shows that within a single-site framework, very different results can be obtained at the extremities of the spectrum whereas converging results are obtained at its centre. Possible extensions to cases where short-range order effects are important, such as in liquid-metal systems, are also discussed.