Energy gaps in disordered systems: II. Alloys

It is shown that, if a band gap in one metal overlaps the corresponding gap in another, then no state exists in the region of overlap in any alloy of the two, provided only that the alloy potential is everywhere intermediate between the potentials of the pure metals. This theorem is related to the work of Saxon and Hutner and of Luttinger. A condition for the existence of band gaps is derived for models not satisfying the conditions of the theorem.