Fano‐Majorana Effect and Bound States in the Continuum on a Crossbar‐Shaped Quantum Dot Hybrid Structure

Transport properties are investigated through a crossbar‐shaped structure formed by a quantum dot (QD) coupled to two normal leads and embedded between two 1D topological superconductors (TSCs). Each TSC hosts Majorana‐bound states (MBSs) at its ends, which can interact between them with an effective coupling strength. A signature of bound states in continuum (BIC) is found in the MBSs spectral function. By allowing finite inter MBSs coupling, BICs splitting is observed and shows projection in transmission for asymmetric coupling case as quasi‐BICs. As a consequence, it is also shown that the Fano effect, arising from interference phenomena between MBSs hybridization trough QD, is observed with a half‐integer amplitude modulation. It is believed that the findings can help to better understand the properties of MBSs and their interplay with QDs.     

Independent Dual-Band Bound States in the Continuum Supported by Double Asymmetric Periodic Gratings in Germanium-Based Structure

Bound states in the continuum (BIC) are localized states coexisting with extended waves in the continuum spectrum and have infinite lifetimes without emitting radiation. In practice, symmetry-protected BIC are usually extended to quasi-BIC by breaking symmetry is commonly employed. A new strategy to realize the dual-band BIC on an all-dielectric metasurface is proposed and experimentally proved. This strategy is based on two inverse-guided modes supported by the double asymmetric periodic gratings (dual-APGs). In the normal incidence condition, the guided modes are bounded as radiation-free dark states due to the symmetric incident field and the symmetric structural geometry. By importing symmetry breaking in adjacent gratings or gaps, the guided modes are coupled with radiation mode and converted into resonance states with a high Q-factor. These two BICs modes supported by air gaps and gratings can be controlled independently. In addition, experimental observation and verification based on the non-etching fabrication technology in the mid-infrared band are also implemented. This work provides a new method for the realization and tuning of dual-frequency BICs, the obtained high Q-factor independent bi-quasi BICs have potential applications in nonlinear optics, multi-mode laser, and optical sensing.     

Two-electron bound states in a continuum in quantum dots

A bound state in a continuum (BIC) might appear in open quantum dots for the variation in the dot’s shape. By means of the equations of motion of the Green’s functions, we investigate the effect of strong intradot Coulomb interactions on that phenomenon within the framework of the impurity Anderson model. The equation that the imaginary part of the poles of the Green’s function equals zero yields the condition for BICs. As a result, we show that the Coulomb interactions replicate the single-electron BICs into two-electron ones. The text was submitted by the authors in English.     

PT Symmetry Induced Rings of Lasing Threshold Modes Embedded with Discrete Bound States in the Continuum

It is well known that spatial symmetry in a photonic crystal(PhC) slab is capable of creating bound states in the continuum(BICs),which can be characterized by topological charges of polarization vortices.Here,we show that when a PT-symmetric perturbation is introduced into the PhC slab,a new type of BICs(pt-BICs) will arise from each ordinary BIC together with the creation of rings of lasing threshold modes with pt-BICs embedded in these rings.Different from ordinary BICs,the Q-factor divergenc...     

Triple Rashba dots as a spin filter: Bound states in the continuum and Fano effect

We propose an efficient spin-filter device by exploiting bound states (BICs) in the continuum and Fano effect on a triple Rashba quantum dot molecule embedded in an Aharonov-Bohm interferometer. We find that the coexistence of a BIC and a Fano antiresonance result in polarizations close to 100% in wide regions in the space of parameters.     

Bound states in the continuum in two-dimensional serial structures

We investigate the occurrence of bound states in the continuum (BICs) in serial structures of quantum dots coupled to an external waveguide, when some characteristic length of the system is changed. By resorting to a multichannel scattering-matrix approach, we show that BICs do actually occur in two-dimensional serial structures, and that they are a robust effect. When a BIC is produced in a two-dot system, BICs also occur for several coupled dots. We also show that the complex dependence of the conductance upon the geometry of the multi-dot system allows for a simple picture in terms of the resonance pole motion in the multi-sheeted Riemann energy surface. Finally, we show that in correspondence to zero-width states for the open system one has a multiplet of degenerate eigenenergies for the associated closed serial system, thereby generalizing results previously obtained for single dots and two-dot structures.     

Friedel phase discontinuity and bound states in the continuum in quantum dot systems

In this Letter we study the Friedel phase of the electron transport in two different systems of quantum dots which exhibit bound states in the continuum (BIC). The Friedel phase jumps abruptly in the energies of the BICs, which is associated to the vanishing width of these states, as shown by Friedrich and Wintgen in [H. Friedrich, D. Wintgen, Phys. Rev. A 31 (1985) 3964]. This odd behavior of the Friedel phase has consequences in the charge through the Friedel sum rule. Namely, if the energy of the BIC drops under the Fermi energy the charge changes abruptly in a unity. We show that this behavior closely relates to discontinuities in the conductance predicted for interacting quantum dot systems.     

人工光学微纳结构中的连续体束缚态:原理、发展及应用

人工微结构可以捕获特定频率的电磁波,其为增强光与物质相互作用以及调控光场的重要平台之一.连续体束缚态在能谱上位于辐射连续区域,其是开放波动系统中与辐射连续态完全正交的本征态.连续体束缚态源于波动的相干相消,可以极大地抑制微纳光子器件的辐射损耗,为解决人工微纳结构中的光束缚提供全新思路.本文回顾连续体束缚态的发展历程,着...     

Bound states in the continuum in metal—dielectric photonic crystal with a birefringent defect

By using the difference of the band structure for the TE and TM waves in the metal—dielectric photonic crystals beyond the light cone and the birefringence of the anisotropic crystal, a one-dimensional photonic system is constructed to realize the bound states in the continuum (BICs). In addition to the BICs arising from the polarization incompatibility, the Friedrich—Wintgen BICs are also achieved when the leaking TM wave is eliminated due to the destructive interference of its ordinary and extraordinary wave components in the anisotropic crystal. A modified scheme favorable for practical application is also proposed. This scheme for BICs may help to suppress the radiation loss in the metal—dielectric photonic crystal systems.     

Bound states in continuum: Quantum dots in a quantum well

We report on the existence of a bound state in the continuum (BIC) of quantum rods (QR). QRs are novel elongated InGaAs quantum dot nanostructures embedded in the shallower InGaAs quantum well. BIC appears as an excited confined dot state and energetically above the bottom of a well subband continuum. We prove that high height-to-diameter QR aspect ratio and the presence of a quantum well are indispensable conditions for accommodating the BIC. QRs are unique semiconductor nanostructures, exhibiting this mathematical curiosity predicted 83 years ago by Wigner and von Neumann.     

Bound states in the continuum in a single-level Fano-Anderson model

Bound states in the continuum (BIC) are shown to exist in a single-level Fano-Anderson model with a colored interaction between the discrete state and a structured tight-binding continuum, which may describe mesoscopic electron or photon transport in a semi-infinite one-dimensional lattice. The existence of BIC is explained in the lattice realization as a boundary effect induced by lattice truncation.     

On electromagnetic fields in the Hamiltonian description of continua

The group theoretical structure of an infinite dimensional Hamiltonian formulation of continuum mechanics is studied using as an example the Maxwell-Vlasov system. In contrast to earlier works, electromagnetism and charged matter are coupled via Poisson brackets without using the vector potential. The charged matter is described on the group of canonical transformations on R⁶ and we show that its evolution arises from a symplectic structure, modified by the magnetic field. The configurations of the electromagnetic field must be constrained by the physical requirement of the Gauss law. With the energy-functional taken as a Hamiltonian this leads - even for relativistic particles - to the well-known equations of motion.     

Evolution of polarization singularities accompanied by avoided crossing in plasmonic system

The evolution of polarization singularities supported in a one-dimensional periodic plasmonic system is studied. The lateral inversion symmetry of the system, which breaks the in-plane inversion symmetry and up-down mirror symmetry simultaneously, yields abundant polarization states. A complete evolution process with geometry for the polarization states is traced. In the evolution, circularly polarized points (C points) can stem from 3 different processes. In addition to the previously reported processes occurring in an isolated band, a new type of C point appearing in two bands simultaneously due to the avoided band crossing, is observed. Unlike the dielectric system with a similar structure which only supports at-$\varGamma$ bound states in the continuum (BICs), accidental BICs off the $\varGamma$ point are realized in this plasmonic system. This work provides a new scheme of polarization manipulation for the plasmonic systems.     

Integrable discrete static Hamiltonian with a parametric double-well potential

A one-dimensional discrete conservative Hamiltonian with a generalized form of the Schmidt potential, is constructed with the help of a non-integrable discrete Hamiltonian whose parametrized double-well potential can be reduced to the ?⁴ potential. The new conservative Hamiltonian is completely integrable in the discrete static regime, and the associate exact nonlinear solution is shown to coincide with the continuum nonlinear periodic solution of the non-integrable Hamiltonian. Numerical simulations and nonlinear stability analysis suggest that the discrete mapping derived from the completely integrable Hamiltonian undergoes a bifurcation which does not leads to the chaotic phase with randomly pinned states, but instead to a phase where real solutions become rare forming a cluster of periodic points around an elliptic fixed point.     

The structure of the gauge theory vacuum

The finite action Euclidean solutions of gauge theories are shown to indicate the existence of tunneling between topologically distinct vacuum configurations. Diagonalization of the Hamiltonian then leads to a continuum of vacua. The construction and properties of these vacua are analyzed. In non-abelian theories of the strong interactions one finds spontaneous symmetry breaking of axial baryon number without the generation of a Goldstone boson, a mechanism for chiral SU(N) symmetry breaking and a possible source of T violation.     

Spectral degeneracy of the lattice dirac equation as a function of lattice shape

We investigate the free Dirac equation in 2 + 1 dimensions on square, triangular, and hexagonal lattices. For each lattice the spectrum exhibits a degeneracy not present in the continuum limit. In the square and hexagonal cases there is a 4-fold degeneracy corresponding to 2 independent symmetries of the Hamiltonian; the degeneracy is eliminated by diagonalizing these symmetries and projecting onto the subspace characterized by a particular pair of eigenvalues. For the triangular case the degeneracy is 6-fold, but the naive Hamiltonian does not possess enough symmetry to eliminate the degeneracy. Certain ambiguities in the lattice Hamiltonian are pointed out and by the addition of terms which vanish in the continuum limit, it is cast in a form with sufficient symmetry to remove the degeneracy entirely, just as was done for the hexagonal and square lattices. It is found that after elimination of the spectral degeneracy the Hamiltonians for the hexagonal and triangular lattices are identical. The solutions to these theories are shown to have the correct continuum limit.     

Off-resonant two-photon-assisted electron transfer between quantum dots

Electron transfer between bound states of remote quantum dots driven by an off-resonant electromagnetic pulse is analyzed. In the case of nearly equal energies of the states, a two-photon transfer mechanism related to the high-frequency off-resonant Stark effect is proposed. An equivalent transformation is used to derive an effective Hamiltonian that provides a basis for correct treatment of continuum (conduction-band) states. It is shown that optimal conditions for electron transfer correspond to quasi-resonant excitation of states near the lower edge of the continuum. The characteristics of the process are evaluated.     

On the structure of the relativistic many-body problem and the construction of effective many-hadron theories

The general structure of the bound state problem posed by a Poincaré-invariant quantum field theory is discussed. It is pointed out that the only present-day method which promises to solve this problem is a nonperturbative regularisation and a check of scaling in the continuum limit. It is demonstrated that perturbation procedures like the Green's function methods of “quantum hadro-dynamics” are inconsistent with respect to covariance and do not solve the bound state problem. As a consequence we propose to use for an effective many-hadron theory a regularised Hamiltonian including form factors, the arbitrariness of which may be essentially restricted by a “minimal relativity” condition. Examples for such effective theories are discussed.     

Decay width and final state in α-decay

If the theory for the decay of a prepared state is formulated in a model-independent way it leads to an equation for the final state. This continuum state is extremely non-resonant and orthogonal to the bound initial state which is used as a prepared state. The decay width is given by the matrix element of the exact Hamiltonian between these two states. Under certain conditions it can be reduced to a matrix element of the residual interaction. From the properties of the final state which are numerically tested with an example in potential scattering, follows the justification for the cluster ansatz in α-decay.