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 forbidden͒. 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.

Theoretical and experimental evidence of Fano-like resonances in simple monomode photonic circuits

“…[4][5][6][7][8][9] Mainly, the subject of these studies was to use these interferometric systems to show the conditions for the existence and the collapse of Fano resonances as function of the applied current voltage and magnetic flux. These studies are also related to the investigation of the electronic states of quantum dots [4][5][6][7][8][9] as well as to the understanding [10][11][12][13] of the transmission phase jumps by p between two adjacent resonances in relation with the experiments of Yacoby et al 14,15 The analogy between scattering properties of electrons and other elementary excitations suggests that this type of feature can also appear in other vibrational systems. 16 When the resonance falls between two anti-resonances, Fano resonance behaves like electromagnetic induced transparency (EIT) resonance.…”

“…In some recent papers, 13,39,68 we have proposed a new simple filter structure to study theoretically Fano resonances for acoustic, mesoscopic, and magnonic 1D circuits. This structure consists of two side stubs, which play the role of resonators, grafted at two sites on an infinite waveguide (see Fig.…”

Transmission gaps and Fano resonances in an acoustic waveguide: analytical model

“…Mainly, the subject of these studies was to use the so-called Aharonov-Bohm interferometric systems to show the conditions for the existence and the collapse of Fano resonances as functions of the applied current voltage and magnetic flux. These studies are also related to the investigation of the electronic states of quantum dots [22,23] as well as to the understanding [25,26] of the transmission phase jumps by π between two adjacent resonances in relation to the experiments of Yacoby et al [27]. The analogy between scattering properties of electrons and phonons suggests that this type of feature can also appear in other vibrational systems [28].…”

Aharonov-Bohm-effect induced transparency and reflection in mesoscopic rings side coupled to a quantum wire

“…These latter resonances are characterized by a peak followed by a dip in the transmission spectra as a consequence of a destructive interference of the waves, giving rise to an asymmetric line shape. These resonances have been the subject of intensive study from the theoretical and experimental point of view in single [47][48][49][50][51][52][53][54][55][56][57] and double [58][59][60][61][62][63][64][65] rings placed between two leads. In addition to Fano resonances, persistent currents are also studied in detail in A-B structures made of one or double rings [47,53,58] in presence of the magnetic flux and impurity or quantum dots in the arms of the ring.…”

“…However, few works have been devoted to EIT resonances in mesoscopic systems. Some of us [57] have studied a one-dimensional loop structure with dangling resonators on both sides. EIT-like resonances have been obtained by tailoring the lengths of the different wires constituting this structure.…”