S-matrix theory for nanostructure resonances

A general theory of coherent propagation of an electron through a multimode nanostructure is developed in terms of the S-matrix connecting the outward mode amplitudes to the inward mode amplitudes. The quasi-local stares and associated transmission/reflection resonances arise from poles of the eigenvalues of the S-matrix as a function of complex electron energy. In a quasi-level's energy range, the density of states within the nanostructure, given by the energy dependence of the associated eigenvalue, is just such as to accommodate one electron in the filled states. The connection with Levinson's theorem, for bound states within the nanostructure, is discussed. © 1995.