Tunneling through discrete levels in the continuum

We study the ballistic transport in quantum channels containing attractive impurities. We show that coherent interaction between asymptotic resonances may cause resonances to disappear and discrete levels to appear in the continuum at certain (critical) values of the parameters of the system. For the first time the tunneling of an electron through discrete levels is investigated. We find that the transmissivity changes dramatically when the scattered electrons at infinity have an energy coinciding with that of the discrete levels. It is found that a new type of degeneracy may arise in the system at critical values of the parameters, a degeneracy in which one state is described by a localized wave function and the other, by a propagating wave function. We calculate the critical values of the parameters of the structure and discuss ways of experimentally implementing this effect in two-dimensional channels. Zh. éksp. Teor. Fiz. 115, 211–230 (January 1999)     

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.     

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.     

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.     

Fano resonances in semiconductor superlattices

We use semiconductor superlattices as a model system for the investigation of Fano resonances. In absorption the excitonic transitions of the Wannier–Stark ladder show the typical asymmetric line shape due to coupling to the continuum of lower-lying transitions. The unique feature of these Fano resonances is that they allow to continuously tune the key parameter – the coupling strength Γ between the discrete state and the degenerate continuum – by varying the bias voltage. Using this feature, we directly show that the Fano coupling leads to a fast polarization decay. We also investigate the dependence of the Fano parameters on the structure of the superlattice and compare with an extensive theoretical model of the resonances.     

Fano resonance in the impurity photoconductivity spectrum of InP doped with shallow donors

The Fano resonances in the impurity photoconductivity spectra of n-InP are investigated theoretically and experimentally. It is shown that the calculations describe the experimental data with an accuracy of up to 20%.     

Mode-matched Fano resonances for all-optical switching applications

We introduce the concept of mode-matched Fano resonances in one-dimensional, subwavelength, diffraction gratings. These resonances are characterized by an extremely high quality (Q)-factor and lend themselves well for applications to ultra-low power, all-optical switching devices at telecommunication wavelengths. We provide examples of diffraction gratings made of a chalcogenide glass (As₂S₃) where, thanks to the mode-matched Fano resonances, all-optical switching is obtained at local field intensities well below the photo-darkening threshold of the material.     

Transport properties of a double quantum dot molecule in the presence of impurity effects

In this Letter, we studied the electronic transport through a parallel-coupled double quantum dot (DQD) molecule including impurity effects at zero temperature. The linear conductance can be calculated by using the Green's function method. An obvious Fano resonance arising from the impurity state in the quantum dot is observed for the symmetric dot-lead coupling structure in the absence of the magnetic flux through the quantum device. When the magnetic flux is presented, two groups of conductance peaks appear in the linear conductance spectra. Each group is decomposed into one Breit-Wigner and one Fano resonances. Tuning the system parameters, we can control effectively the shapes of these conductance peaks. The Aharonov-Bohm (AB) oscillation for the magnetic flux is also studied. The oscillation period of the linear conductance with π, 2π or 4π may be observed by tuning the interdot tunneling coupling or the dot-impurity coupling strengths.     

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.     

Effects of intrasubband coupling on the scattering phases and density of states in a quantum wire

The properties of scattering phases and density of states in a quantum wire with an attractive scatterer are analyzed. We consider two bound states which couple to a scattering channel and give rise to two Fano resonances. It is shown that varying the parameters of the scatterer (such as its strength and position) produces significantly different effects on the phase behavior and density of states, depending on the subband they occur. These effects stem mainly from the difference between the coupling matrix elements of the two resonant levels with the propagating channel mode.     

Spatial effects of Fano resonance in local tunneling conductivity in vicinity of impurity on semiconductor surface

We present the results of local tunneling conductivity spatial distribution detailed theoretical investigations in vicinity of impurity atom for a wide range of applied bias voltage. We observed Fano resonance in tunneling conductivity resulting from interference between resonant tunneling channel through impurity energy level and direct tunneling channel between the tunneling contact leads. We have found that interference between tunneling channels strongly modifies form of tunneling conductivity measured by the scanning tunneling microscopy/spectroscopy (STM/STS) depending on the distance value from the impurity.     

Fano effect in a double T-shaped interferometer

We study the coherent transport in a one-dimensional lead with two side-coupled quantum dots using the Keldysh’s Green function formalism.The effect of the interdot Coulomb interaction is taken into account by computing the firstand second order contributions to the self-energy.We show that the Fano interference due to the resonance of one dotis strongly affected by the fixed parameters that characterize the second dot. If the second dot is tuned close to resonance an additionalpeak develops between the peak and dip of the Fano line shape of the current. In contrast, when the second dotis off-resonance and its occupation number is close to unity the interdot Coulomb interaction merely shifts the Fano line and no other maxima appear.The system we consider is more general than the single-dot interferometer studied experimentally by Kobayashi et al. [Phys. Rev. B 70, 035319 (2004)] and may be used for controlling quantum interference and studying decoherence effects in mesoscopic transport.     

Dark and bright mode hybridization: From electric to magnetic Fano resonances

The excitation of plasmonic Fano resonances leads to a dual advantage in nano-photonics, in terms of local field enhancement and far-field spectral selectivity. Nevertheless, a remarkable challenge related to the hybridization between bright and dark plasmonic modes, i.e. between the two elements cooperating to the Fano resonance generation, consists in the sub-wavelength activation of dark modes via near-field channel. In this regard, strongly coupled plasmonic nano-assemblies are ideal systems providing a highly efficient way towards their excitation. Here, we analyze two trimer nano-architectures supporting respectively electric and magnetic Fano resonances. The different approaches employed for describing the two systems highlighted the role that the near-field coupling and the LSPs de-phasing separately play in the Fano hybridization phenomena.     

Characteristics and mechanism analysis of Fano resonances in Π-shaped gold nano-trimer

Fano interference of metallic nanostructure is an effective way to reduce the irradiation loss and improve the spectral resolution. A Π-shaped gold nano-trimer, which is composed of a gold nanorod and two gold nanorices, is presented to investigate the properties of Fano resonances in the visible spectrum by using the finite element method(FEM). The theoretical analysis demonstrates that the Fano resonance of the Π-shaped gold nano-trimer is attributed to the near-field interaction between the bright mode of the nanorice pair and the dark quadrupole mode of the nanorod. Furthermore, by breaking the geometric symmetry of the nanostructure the line-shape spectrum with double Fano resonances of Π-shaped gold nano-trimer is obtained and exhibits structure-dependent and medium-dependent characteristics. It is a helpful strategy to design a plasmonic nanostructure for implementing multiple Fano resonances in practical applications.     

Refractive index sensing of double Fano resonance excited by nano-cube array coupled with multilayer all-dielectric film

We propose a hybrid structure of a nano-cube array coupled with multilayer full-dielectric thin films for refractive index sensing.In this structure,discrete states generated by two-dimensional grating and continuous states generated by a photonic crystal were coupled at a specific wavelength to form two Fano resonances.The transmission spectra and electric field distributions of the structure were obtained via the finite-difference time-domain method.We obtained the optimal structural parameters after optimizing the geometrical parameters.Under the optimal parameters,the figure of merit(FOM)values of the two Fano resonances reached 1.7×10⁴and 3.9×10³,respectively.These results indicate that the proposed structure can achieve high FOM refractive index sensing,thus offering extensive application prospects in the biological and chemical fields.     

Resonance scattering in quantum wells with nanocenters

It is shown that, in 2D electron layers, nanocenters of finite radius (quantum dots, donors) may give rise to Fano resonances in the scattering cross section. The resonance contribution to the residual resistance is calculated.     

Two-state double-continuum Fano resonance at the Si(100) surface

Fano resonances are well-known manifestations of the interference between a direct and an indirect ionization process. Here we report on a more complicated interference pattern observed in two-photon photoemission at the Si(100) surface. This two-dimensional Fano profile involves two discrete surface resonances which couple as initial and intermediate states to the silicon valence and conduction band, respectively. Tuning the photon energy across the surface resonance reveals asymmetric line profiles with pronounced destructive interference in the two-photon photoelectron intensities of both initial and intermediate states. The interference pattern is explained by an analytic extension of Fano's model to describe the coupling of two discrete states with two continua. This coupling strongly modifies the photoabsorption and is of general importance for light conversion in nanostructures and light-harvesting devices.     

Resonance features of the conductance of open billiards: Spin-orbit coupling effects

Transport properties of an open circular billiard with attached channels in the presence of the spin-orbit coupling are studied. It is shown that the inclusion of the spin-orbit coupling causes the occurrence of additional narrow Fano resonances on the energy dependence of the conductance. It is established that the resonance regions are associated with the energy levels in a corresponding closed billiard. The effect of small finite temperatures on the observability of the conductance resonances is estimated.     

Fano resonances in complex plasmonic super-nanoclusters: The effect of environmental modifications on the LSPR sensitivity

In this study, gold nanodisk clusters in heptamer orientations as clusters were used to design a super-heptamer consisting of one central and six peripheral heptamers. We examined the position and movement of the plasmon and Fano resonances by sketching the spectral response of the superstructure for various nanodisk dimensions. The quality of the interference between the superradiant and subradiant plasmon resonance modes of the nanodisk clusters was found to depend strongly on the structural configuration and the refractive index of the environmental medium. We replaced the central heptamer with a nanodisk and probed the position of the Fano resonance by geometrically altering the nanodisk structure. Finally, the effect of the dielectric environment on the plasmon response of both of the studied structures was examined numerically and theoretically. The localized surface plasmon resonance sensitivity of the finite plasmonic structures to the presence of liquid substances was investigated and shown by plotting the linear figure of merit. The finite-difference time-domain method was used as a numerical tool to investigate the plasmon response of the structure.     

Multiple resonances and Coulomb blockade splitting in a quantum dot-DNA composite

Inspired by the recent realizations of quantum dot (QD)-DNA conjugation, we study the spectral density of a magnetic impurity coupled to a mesoscopic semiconducting host. Using a combination of exact diagonalization technique and an analytic approach, we demonstrate that various types of resonances occur according to the relative position of impurity levels (IL) with respect to the host levels (HL). While the usual Coulomb peaks appear when the IL lie inside a band gap, with IL approaching HL and hybridization activated, they shift nonlinearly with the repulsion strength and even undergo splitting for a strong hybridization. When IL merge into HL, multiple resonances of a comblike structure are found along with a parity effect.