We investigate the occurrence of bound states in the continuum (BIC's) 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 BIC's 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, it also occurs for several coupled dots. We also show that the complex dependence of the conductance upon the geometry of the device 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 a zero--width state 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 devices.
In this work, we consider a single-level quantum dot (QD) and a Majorana bound state (MBS) placed at the end of a topological superconducting nanowire (TSW). Both are coupled to the continuum and do not have a direct connection between them. We addressed the behavior of MBS leaking phenomena and its consequences into the QD physics in non-interacting and Coulomb blockade regime. By employing Green's function formalism via the equation of motion procedure, we calculate the physical quantities of interest. Our results show that the leakage of the MBS into the continuum state is achieved and can …
We report the formation of bound states in the continuum for Dirac-like fermions in structures composed by a trilayer graphene flake connected to nanoribbon leads. The existence of this kind of localized states can be proved by combining local density of states and electronic conductance calculations. By applying a gate voltage, the bound states couple to the continuum, yielding a maximum in the electronic transmission. This feature can be exploited to identify bound states in the continuum in graphene-based structures.
We discuss the relation between continuum bound states (CBS) localized on a defect, and surface states of a finite periodic system. We use the transfer matrix method to model an experiment of Capasso, and find all continuum bound and anti-bound states. We compute the rate for intra-subband transitions from the ground state to the CBS and derive a sum rule. Finally we show how to improve the confinement of a CBS while keeping the energy fixed.
The existence of bound states in the continuum was predicted at the dawn of quantum mechanics by von Neumann and Wigner. In this work we discuss the mechanism of formation of these exotic states and the feasibility to observe them experimentally in symmetrical heterostructures composed by segments of graphene ribbons with different widths forming a graphene quantum dot. We identify the existence of bound states in the continuum in these graphene quantum dot systems by means of local density of states and electronic conductance calculations.
We generalize our recent results for the boundary and interface charges in one-dimensional single-channel continuum [Phys. Rev. B 104, 155409 (2021)] and multichannel tight-binding [Phys. Rev. B 104, 125447 (2021)] models to the realm of the multichannel continuum systems. Using the technique of boundary Green's functions, we give a rigorous proof that the change in boundary charge upon the shift of the system towards the boundary by the distance $x_φ\in[0, L]$ is given by a perfectly linear function of $x_φ$ plus an integer-valued topological invariant $I$ -- the so called boundary invariant.…
In this paper we study the formation of bound states in the continuum in a quantum dot molecule coupled to leads. Based in the combination of bound states in the continuum and Fano effect, we propose a new design of a spin-dependent polarizer. By lifting the spin degeneracy of the carriers in the quantum dots by means of a magnetic field the system can be used as a spin-polarized device. A detailed analysis of the spin-dependent conductance and spin polarization as a function of the applied magnetic field and gate voltages is carried out.
We consider quantum transmission through double-bend $Π$- and $Z$-shaped waveguides controlled by the finger gate potential. Using the effective non-Hermitian Hamiltonian approach we explain the resonances in transmission. We show a difference in transmission in the short waveguides that is the result of different chirality in $Z$ and $Π$ waveguides. We show that the potential selectively affects the resonant widths resulting in the occurrence of bound states in the continuum.
Bound state in continuum (BIC) might appear in open quantum dots for variation of the dot's shape. By means of the equations of motion of Green functions we investigate effect of strong intradot Coulomb interactions on that phenomenon in the framework of impurity Anderson model. Equation that imaginary part of poles of the Green function equals to zero gives condition for BICs. As a result we show that Coulomb interactions replicate the single-electron BICs into two-electron ones.
We study bound states embedded into the continuum of edge states in two-dimensional topological insulators. These states emerge in the presence of a short-range potential of a structural defect coupled to the boundary. In this case the edge states flow around the defect and have two resonances in the local density of states. The bound state in continuum (BIC) arises due to an interference of the resonances when they are close to the degeneracy. We find the condition under which the BIC appears, study the spacial distribution of the electron density, and show that the BIC has a helical structur…
Using formalism of effective Hamiltonian we consider bound states in continuum (BIC). They are those eigen states of non-hermitian effective Hamiltonian which have real eigen values. It is shown that BICs are orthogonal to open channels of the leads, i.e. disconnected from the continuum. As a result BICs can be superposed to transport solution with arbitrary coefficient and exist in propagation band. The one-dimensional Aharonov-Bohm rings that are opened by attaching single-channel leads to them allow exact consideration of BICs. BICs occur at discrete values of energy and magnetic flux howev…
Bound states in the continuum (BICs) are counter-intuitive localized states with eigenvalues embedded in the continuum of extended states. Recently, nontrivial band topology is exploited to enrich the BIC physics, resulted in topological BICs (TBICs) with extraordinary robustness against perturbations or disorders. Here, we propose a simple but universal mirror-stacking approach to turn nontrivial bound states of any topological monolayer model into TBICs. Physically, the mirror-stacked bilayer Hamiltonian can be decoupled into two independent subspaces of opposite mirror parities, each of whi…
We reveal that metasurfaces created by seemingly different lattices of (dielectric or metallic) meta-atoms with broken in-plane symmetry can support sharp high-$Q$ resonances that originate from the physics of bound states in the continuum. We prove rigorously a direct link between the bound states in the continuum and the Fano resonances, and develop a general theory of such metasurfaces, suggesting the way for smart engineering of resonances for many applications in nanophotonics and meta-optics.
We examine bulk and surface bound states in the continuum (BIC) that is, square-integrable, localized modes embedded in the linear spectral band of a discrete lattice including interactions to first-and second nearest neighbors. We suggest an efficient method for generating such modes and the local bounded potential that supports the BIC, based on the pioneering Wigner-von Neumann concept. It is shown that the bulk and surface embedded modes are structurally stable and that they decay faster than a power law at long distances from the mode center.
We demonstrate the existence of tunable bound-states in continuum (BIC) in a 1-dimensional quantum wire with two impurities induced by an intense monochromatic radiation field. We found that there is a new type of BIC due to the Fano interference between two optical transition channels, in addition to the ordinary BIC due to a geometrical interference between electron wave functions emitted by impurities. In both cases the BIC can be achieved by tuning the frequency of the radiation field.
We study, both theoretically and experimentally, tunable metasurfaces supporting sharp Fano-resonances inspired by optical bound states in the continuum. We explore the use of arsenic trisulfide (a photosensitive chalcogenide glass) having optical properties which can be finely tuned by light absorption at the post-fabrication stage. We select the resonant wavelength of the metasurface corresponding to the energy below the arsenic trisulfide bandgap, and experimentally control the resonance spectral position via exposure to the light of energies above the bandgap.
We show that finite lattices with arbitrary boundaries may support large degenerate subspaces, stemming from the underlying translational symmetry of the lattice. When the lattice is coupled to an environment, a potentially large number of these states remains weakly or perfectly uncoupled from the environment, realising a new kind of bound states in the continuum. These states are strongly localized along particular directions of the lattice which, in the limit of strong coupling to the environment, leads to spatially-localized subradiant states.
We present a distinct mechanism for the formation of bound states in the continuum (BICs). In chiral quantum systems there appear zero-energy states in which the wave function has finite amplitude only in one of the subsystems defined by the chiral symmetry. When the system is coupled to leads with a continuum energy band, part of these states remain bound. We derive some algebraic rules for the number of these states depending on the dimensionality and rank of the total Hamiltonian. We examine the transport properties of such systems including the appearance of Fano resonances in some limitin…
We report a bound state of the one-dimensional two-particle (bosonic or fermionic) Hubbard model with an impurity potential. This state has the Bethe-ansatz form, although the model is nonintegrable. Moreover, for a wide region in parameter space, its energy is located in the continuum band. A remarkable advantage of this state with respect to similar states in other systems is the simple analytical form of the wave function and eigenvalue. This state can be tuned in and out of the continuum continuously.
