Interference of quantum states in electronic waveguides with impurities

Effects of interference between propagating and localized states in quasi-one-dimensional electronic waveguides containing finite-size attracting impurities (quantum dots) are investigated. The electron scattering matrix is calculated in the framework of the Feshbach theory H. Feshbach, Ann. Phys. 5, 357 (1958); Ann. Phys. 19, 287 (1962)], when resonant states in closed channels are taken into account exactly, while non-resonant states are taken into account in perturbation theory. It is shown that finite-size attracting impurities may generate a series of asymmetric Fano resonances in the waveguide transmission. As a result of interference of electron states, the characteristics of resonances may oscillate upon a change in the impurity parameters. The conditions are determined under which the interference of an electron wave leads to a “collapse” and “swing” of Fano resonances.