Validity of the recursion method for calculating the energy gap of (GaAs)1−xGe2x: Comments on a paper by Gu, Newman, and Fedders

We have shown previously that the energy gap of (GaAs${)}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{Ge}}_{2\mathrm{x}}$, as calculated by the recursion method, is sensitive to the presence of As-As nearest-neighbor pairs. When significant concentrations of such As-As bonds are incorporated into alloys with near-midrange compositions the gap decreases from about 0.5 eV, in agreement with optical-absorption data, to zero, in clear disagreement with experiment. This provides a strong reason for rejecting the Newman-Dow (ND) thermodynamic model of the alloy, which predicts large concentrations of As-As bonds. In a recent paper Gu, Newman, and Fedders claimed that the recursion calculations, upon which our rejection of the ND model is based, are invalidated by an elementary error. We demonstrate that this assertion is unfounded.