Transmission gaps and sharp resonant states in the electronic transport through a simple mesoscopic device

Abstract

A simple electronic circuit consisting of a single symmetric or asymmetric loop with dangling resonators is designed to obtain possibly large stop bands (where the propagation of electrons is forbidden). Contrary to all known systems of this kind, a spectral transmission gap of nonzero width occurs here even with a single loop. This is obtained by combining appropriately the zeros of transmission of the loop and of the dangling resonators. Sharp resonant electronic states inside the gaps can be achieved without introducing any defects in the structure. This results from an internal resonance of the structure when such a resonance is situated in the vicinity of a zero of transmission or squeezed between two zeros of transmission, the so-called Fano resonances. A general expression for the transmission coefficient is given for various systems of this kind within the framework of the interface response theory. The amplitude and the phase of the transmission are discussed as a function of the wave vector or energy and it is shown that the width of the stop bands is very sensitive to the number of grafted resonators, while the magnitude of the resonant states in the transmission coefficient is very sensitive to the lengths of the different arms constituting the loop and the dangling resonators. These structures may have potential applications in microelectronic devices.