Transmission gaps,trapped modes and Fano resonances in Aharonov–Bohm connected mesoscopic loops

A simple mesoscopic structure consisting of a double symmetric loops coupled by a segment of length $d_0$ in the presence of an Aharonov–Bohm flux is designed to obtain transmission band gaps and Fano resonances. A general analytical expression for the transmission coefficient and the density of states (DOS) are obtained for various systems of this kind within the framework of the Green's function method in the presence of the magnetic flux. In this work, the amplitude of the transmission and DOS are discussed as a function of the wave vector. We show that the transmission spectrum of the whole structure may exhibit a band gap and a resonance of Fano type without introducing any impurity in one arm of the loop. In particular, we show that for specific values of the magnetic flux and the lengths of the arms constituting the loops, the Fano resonance collapses giving rise to the so-called trapped states or bound in continuum (BIC) states. These states appear when the width of the Fano resonance vanishes in the transmission coefficient as well as in the density of states. Also, we show that the shape of the Fano resonances and the width of the band gaps are very sensitive to the value of the magnetic flux and the geometry of the structure. These results may have important applications for electronic transport in mesoscopic systems.     

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.     

Beating oscillation and Fano resonance in the laser assisted electron transmission through graphene δ-function magnetic barriers

We investigate theoretically the transmission of electrons through a pair of δ-function magnetic barriers in graphene in presence of external monochromatic, linearly polarized and CW laser field. The transmission coefficients are calculated in the framework of non-perturbative Floquet theory using the transfer matrix method. It is noted that the usual Fabry–Perot oscillations in transmission through the graphene magnetic barriers with larger inter barrier separation takes the shape of beating oscillations in presence of the external laser field. The laser assisted transmission spectra are also found to exhibit the characteristic Fano resonances (FR) for smaller values of the inter barrier separation. The appearance of the perfect node in the beating oscillation and the asymmetric Fano line shape can be controlled by varying the intensity of the laser field. The above features could provide some useful and potential information about the light - matter interactions and may be utilized in the graphene based optoelectronic device applications.     

Simple nanometric magnon multiplexer

We study, in the frame of the discrete dipole approximation, the magnons propagation through a simple multiplexing device made of chains of magnetic nanoparticles along which a small chains (called a resonators) is attached. We show that this simple structure can transfer with selectivity one magnon frequency from one chain to the other, leaving neighbour magnonic frequencies unaffected. With an appropriate choice of the geometrical (or magnetic) parameters of the structure, it is possible to control the desired magnon ejection. A general analytical expression for the transmission coefficient is given for various structures of this kind within the framework of the Green’s function method. The amplitude, the phase, and the phase time of the transmission are discussed as a function of frequency. These results may opens new perspectives for constructing, more efficient and more compact, magnonic devices such as narrow-frequency microwave multiplexers.     

Energy dependent spin filtering by using Fano effect in open quantum rings

An open quantum ring containing magnetic quantum structures which is subjected to the Rashba spin–orbit coupling and Zeeman effect is considered. One dimensional quantum wave guide theory is developed and Transfer matrix method in conjunction with spin-dependent Griffith’s boundary condition is used to calculate the transmission coefficients of the corresponding one-electron scattering problem. Investigations into spin-dependent transport show the characteristic oscillations which are affected by impurities. The existence of Rashba spin–orbit coupling leads to the appearance of Fano resonances in transport. The results indicate that the orientation of Fano line shapes is under the influence of impurities. Also, it is shown that by using Fano resonances the system under study can be used as a cent percent spin-filtering device. The spin-filtering property of this system as a function of energy is affected by impurities and can be used in order to design optimized nanodevices.     

Analysis of the phase lapse problem in closed interferometers

We investigate the connection between the asymmetry of the Fano resonances in a mesoscopic interferometer with an embedded quantum dot and the π lapses in the phase of the “bare” dot transmittance. Consecutive Fano resonances with the same (opposite) sign of the Fano parameter imply the presence (absence) of a phase lapse with π between the corresponding resonances of the dot. Our results suggest that the famous “phase lapse” problem, first reported by Schuster et al. [R. Schuster, E. Buks, M. Heiblum, D. Mahalu, V. Umansky, H. Shtrikman, Nature 385 (1997) 417], can therefore be experimentally addressed in closed interferometers. It is also proposed that the Fano effect can be used to extract the phase distributions of the eigenfunctions for a mesoscopic 2D shape, via the parity of the resonances. In the presence of electron–electron interaction, one can calculate the phases of the T-matrix elements. The numerical results lead to the same conclusions as for the non-interacting case.     

Spin-polarized transport through a time-periodic non-magnetic semiconductor heterostructure

Spin-dependent Floquet scattering theory is developed to investigate the photon-assisted spin-polarized electron transport through a semiconductor heterostructure in the presence of an external electric field. Spin-dependent Fano resonances and spin-polarized electron transport through a laser irradiated time-periodic non-magnetic heterostructure in the presence of Dresselhaus spin-orbit interaction and a gate-controlled Rashba spin-orbit interaction are investigated. The electric field due to laser along with the spin-orbit interactions help to get spin-dependent Fano resonances in the conductance, whereas the external bias can be appropriately adjusted to get a near 80% spin-polarized electron transmission through heterostructures. The resultant nature of the Floquet scattering depends on the relative strength of these two electric fields.     

Optical Fiber Excitation of Fano Resonances in a Silicon Microsphere

In this article, Fano lineshape whispering gallery modes were observed in the light scattering spectrum of a silicon microsphere in near-infrared telecommunication wavelengths. A simple model is presented to explain the transition from Lorentzian lineshape to the Fano lineshape resonances with the coupled-mode theory of multiple whispering gallery modes. Polar mode spacing of 0.23 nm is observed in the spectra, which correlates well with the calculated value. The quality factor of the Lorentzian and Fano resonances are on the order of 10⁵. By using an appropriate interface design for the microsphere coupling geometries, Fano lineshape optical resonances herald novel device applications for silicon volumetric lightwave circuits.     

Fano resonances as a probe of phase coherence in quantum dots

In the presence of direct trajectories connecting source and drain contacts, the conductance of a quantum dot may exhibit resonances of the Fano type. Since Fano resonances result from the interference of two transmission pathways, their line shape (as described by the Fano parameter q) is sensitive to dephasing in the quantum dot. We show that under certain circumstances the dephasing time can be extracted from a measurement of q for a single resonance. We also show that q fluctuates from level to level, and we calculate its probability distribution for a chaotic quantum dot. Our results are relevant to recent experiments by G?res et al. [Phys. Rev. B 62, 2188 (2000)].     

Collapse of resonance in quasi-one-dimensional quantum channels

We study the resonance structure of the conductance (transmissivity) of a quasi-one-dimensional channel that contains an attractive impurity of finite dimensions and derive an exact expression for the scattering matrix. We show that an impurity of finite dimensions may cause a set of Fano resonances to appear in the transmissivity. We also find that due to the coherent interaction the Fano resonances can collapse and discrete levels may appear in the continuum. Finally, we establish the wave function of the discrete levels and study the channel transmissivity in the critical regime. Zh. éksp. Teor. Fiz. 116, 263–275 (July 1999)     

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.     

On the spontaneous-coherence-transfer-induced sign change of a sub-natural-width nonlinear resonance

A simple theoretical model is proposed which describes the positive sign of the nonlinear absorption resonances in the experiments of Akul’shin et al. [Phys. Rev. A 57, 2996 (1998)]. An analytical expression for the linear response to a weak probe field is obtained in the weak-saturation limit. It is shown that the positive sign of sub-natural-width resonances is due to the spontaneous transfer of low-frequency coherence from an excited level to the ground state. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 11, 776–781 (10 June 1999)     

Supercurrent and its Fano effect in a Josephson Aharonov-Bohm ring

The Josephson current through an Aharonov-Bohm (AB) interferometer, in which a quantum dot (QD) is situated on one arm and a magnetic flux Φ threads through the ring, has been investigated. In the presence of the magnetic flux, the relation between the Josephson current and the superconductor phase is complex, and the system can be adjusted to π junction by either modulating the magnetic flux or the QD’s energy level ε_d. Due to the electron-hole symmetry, the Josephson current I has the property I(ε_d,Φ)=I(-ε_d,Φ+π). The Josephson current exhibits a jump when a pair of Andreev bound states aligns with the Fermi energy. The condition for the current jump is given. Particularly, we find that the position of the current jump and the position of the maximum value of the critical current I_c are identical. Due to the interference between the two paths, the critical current I_c versus the QD’s level ε_d shows a typical Fano shape, which is similar to the Fano effect in the corresponding normal device. However they also show some differences. For example, the critical current never reaches zero for any parameters, while the current in the normal device can reach zero at the destruction point.     

Fano resonances and electron localization in heterobarriers

A study is made of electron tunneling in semiconductor heterostructures having a complex dispersion law. A generalized Fabry-Perot approach is used to describe tunneling across the barrier. Mixing of electron states at the heterojunctions is responsible for the asymmetric resonant structure of the transmission which is characterized by a resonance-antiresonance pair. The resonance corresponds to a pole while the antiresonance corresponds to a zero of the scattering amplitude in the complex energy plane, i.e., near the pole and the zero the transmission of the heterobarrier has a Fano resonance structure. It is shown that for certain barrier parameters the resonances may collapse and localized states may appear in the heterobarrier, which is observed on the current-voltage characteristics of the barriers. The two-valley model of a GaAs/Al_xGa_1?x As/GaAs heterostructure is considered as an example. An analysis is made of the resonance structure in the barrier as a function of the type of boundary conditions used for the heterojunctions. The low-temperature current-voltage characteristic of the barrier is calculated.     

Spin-dependent Fano effect through parallel-coupled double quantum dots

Based on the nonequilibrium Green' function method, the spin-dependent Fano effect through parallel-coupled double quantum dots has been investigated by taking account of both Rashba spin-orbit interaction and intradot Coulomb interaction. It is shown that the quantum interference through the bonding, antibonding states and through their Coulomb blockade counterparts may result in two Breit-Wigner resonances and two Fano resonances in the conductance spectra. Moreover, the Fano lineshape of the two spin components can be modulated by Rashba spin-orbit interaction when the magnetic flux is switched on.     

Spin-dependent Breit-Wigner and Fano resonances in photon-assisted electron transport through a semiconductor heterostructure

We theoretically investigate the electron transmission through a seven-layer semiconductor heterostructure with the Dresselhaus spin-orbit coupling under two applied oscillating fields. Numerical results show that both of the spin-dependent symmetric Breit-Wigner and the asymmetric Fano resonances appear and that the properties of these two types of resonance peaks are dependent on the amplitude and the relative phases of the two applied oscillating fields. The modulation of the spin-polarization efficiency of transmitted electrons by the relative phase is also discussed.     

Effect of a weak magnetic field on resonant features of conductance in an open circular billiard with Dresselhaus spin-orbit interaction

The effect of a weak magnetic field on the transport properties of an open circular billiard with attached channels in the presence of Dresselhaus spin-orbit interaction are considered. It is shown that the application of a magnetic field leads to splitting of the Fano resonances, which were found earlier on the energy dependence of conductance, into pairs of resonances with half lower amplitudes. The relationship between the energy values to which these resonances collapse when the spin-orbit interaction is absent, and the levels of the energy spectrum in the corresponding closed billiard has been established. It is shown also that the applied magnetic field induces a qualitative change in the spin polarization of a wave in the output channel.     

Supernarrow saturated absorption resonances in weakly coupled two resonant optical cavities

The advantages of the weakly coupled two resonant optical cavities (hereinafter referred to as three-mirror cavity) used for observation of the supernarrow saturated absorption resonances are shown. Among these advantages we can name: (a) the possibility to control the intensity in the cavity with the inside absorbing cell which is important when the gain and absorption saturation parameters differ significantly; (b) the resonances observation from the ‘passive’ side of the three-mirror cavity permits us to decrease drastically the influence of the reflected signal from the detector; (c) if instead of the absorbing cell an active system is put in (gain plus absorption), it is possible by tuning the operating mode of the active interferometer to obtain many-fold gain of the supernarrow resonance amplitude. Received: 11 January 2000 / Revised version: 20 June 2000 / Published online: 9 February 2001     

Instabilities and quasi-localized states in nonlinear Fano-like systems

We study the dynamical scattering in one-dimensional systems with a nonlinear side-coupled defect. Such structures exhibit the nonlinear Fano resonances, where nothing can propagate through. We developed a numerical model to study dynamical scattering. According to our analysis the scattering waves become dynamically unstable in the vicinity of the nonlinear Fano resonances, due to modulational instability caused by the presence of nonlinearity. It results in a time-growing amplitude of the nonlinear defect. We also demonstrate the existence of the nonlinear quasi-localized state, supported by such structures.     

Resonant tunneling through a two-dimensional nanostructure with connecting leads

Ballistic electron transport through a two-terminal nanodevice is considered. An explicit formula is derived for the transmission coefficient of an electron as a function of its energy. An equation for the parameters of the Breit-Wigner and Fano resonances is obtained. Conditions are found under which a collapse of Fano resonances is observed. The effect that the parameters and the arrangement of contacts have on the transport properties of a system is investigated.