Electronic transmission through a ladder with a single side-attached impurity

We study the electronic transmission of a model system composed by two coupled chains with an impurity attached to one of them. Analytical espressions for the transmittivity and for the diagonal and the off-diagonal Green's function matrix elements are derived. Green's function behaviour as function of the charge carrier energy is exploited to interpret the system transmittivity calculated by the scattering matrix formalism. We find that while a single substitutional impurity in the ladder may generate a Fano resonance in the transmittivity in the lower or in the higher energy part of the spectrum, in the case of a single side-attached impurity to the ladder, a resonance is found in each energy region. We interpret such resonances in terms of local density of states and off-diagonal Green's function matrix elements.