ELECTRON DYNAMICS IN GRADED NANOSTRUCTURES

In this paper I describe recent work, jointly with M. Geller, treating the dynamics of electrons in semiconducting alloys, such as AlcGa1-cAs, whose compositions, characterized by c, is a slowly varying function of position: \del(c)(r)\b<<1, where b is a characteristic lattice spacing. The mathematical framework is provided by the so-called generalized Wannier functions (GWF) a(n,l(r) where n and l are band and site labels (for composite bands an additional label v is needed). The GWFs are generalizations to non-periodic systems of the traditional Wannier functions for periodic systems. We show that the eigenstates and frequency-dependent electric response functions can be completely described in terms of two quantities, epsilon(n)(k;C) and p(nm),(k;c), the energy and momentum matrix elements of the uniform alloys of concentrations c, ranging over the values of c in the non-uniform system under consideration.