Theory of Impurity States in Zero-Gap Semiconductors

A theory of impurity states in zero-gap semiconductors is developed. For explicitness we consider a donor impurity with one excess electron. In addition to a statically screened Coulomb potential we assume a highly localized central-cell coupling. This focuses attention on the $s$ states in the discrete hydrogenic spectrum, which are found to have been shifted in energy and broadened into resonant states by the central-cell coupling. For a simple form of the conduction and valence bands we derive equations for determining the positions of these resonant states and their widths.