Bound electron states in the monolayer gapped graphene with the short-range impurities

Bound electron states in impure graphene with the massive Dirac spectrum are considered. Short-range perturbations for defect and impurities of the types “local chemical potential” and “local gap” are taken into account.     

Bound states of linear defects in biaxial nematics and superfluid liquids

It is shown that linear defects in biaxial nematics may form dynamically stable bound states if these defects are linked, almost parallel, and repel one another. Such a situation is possible for pairs of linear defects with a certain topology. This effect can also be observed for nearly parallel vortices in superfluid liquids and superconductors.     

Bound and virtual bound states in semiconductor quantum wells

The bound and virtual bound (resonant) levels of GaAs-Ga(Al)As double quantum wells are calculated within the framework of the envelope function approach. The theoretical work, taken together with the results of excitation spectroscopy measurements, indicates the participation of a light hole virtual bound state in an optical transition.     

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.     

Helical liquids and Majorana bound states in quantum wires

We show that the combination of spin-orbit coupling with a Zeeman field or strong interactions may lead to the formation of a helical electron liquid in single-channel quantum wires, with spin and velocity perfectly correlated. We argue that zero-energy Majorana bound states are formed in various situations when such wires are situated in proximity to a conventional s-wave superconductor. This occurs when the external magnetic field, the superconducting gap, or, most simply, the chemical potential vary along the wire. These Majorana states do not require the presence of a vortex in the system. Experimental consequences of the helical liquid and the Majorana states are also discussed.     

Bound states and equation of state for nondegenerate quantum systems with short-range interactions

The influence of bound states on the second virial coefficient for systems with short-range interactions is investigated, and the equation of state is determined by different methods. The dissociation equilibrium between bound and free particles is discussed.     

Corresponding states theory for the prediction of surface tension of ionic liquids

The surface tension of ionic liquids is studied according to phenomenological scaling and the law of corresponding states. The reduced coordinates γ*–T*, where γ* represents the reduced surface tension and T* is the reduced temperature, are introduced for the prediction of the surface tension from the melting point up to boiling point. It has been shown that the correlation can be expressed as a unique straight-line plot with a linear correlation coefficient of 0.984 that requires only the melting and boiling point parameters and can predict the surface tension accurately.     

The effect of bulk impurities on localized surface states

The effect of the occurrence of bulk impurities in a crystal on the existence and localization of surface states is examined by investigating a simple one-dimensional model. It is found that the bulk impurity has a small effect on the existence conditions for localized states associated with the surface, but the degree of localization of the corresponding charge density can be altered appreciably by the presence of such impurities. The penetration depth associated with localized surface levels can be much greater that than estimated for a pure crystal. The charge density associated with the electrons which occupy localized surface states may vary in a real crystal over a broader region near the surface than would be deduced from models of pure crystals. This will affect physical quantities, such as surface impedance, which are dependent on this charge distribution.     

Photoconductor surface states and detective quantum efficiency

Qualitative phenomenological considerations on photoelectronic processes in a photoconductor microcrystal, envisaged as an individual radiation detector in a photographic system, lead to the anticipation of requirements to be fulfilled in a future silver-free microdetector of high sensitivity. The construction of suitable surface states and the suppression of coulombic factors in recombination processes are expected to be essential.     

Bound states of Dirac electrons in a graphene-based magnetic quantum dot

We investigate the magnetically confined states of the massless Dirac fermions in a graphene quantum dot formed by the inhomogeneous distributions of the magnetic fields inside and outside the dot. The calculated energy spectrum exhibits quite different features with and without the magnetic field inside the dot. It is found that the degeneracy of the relativistic Landau level with negative angular momenta can be lifted, and this degeneracy breaking can be modulated by the magnetic field inside the dot. Moreover, such a system can form the strongly localized states within the dot and along its boundary, especially with the magnetic field inside the dot.     

Bound states in disclinated graphene with Coulomb impurities in the presence of a uniform magnetic field

In this contribution, we study the effects caused by an impurity on the quantum dynamics of massive excitations in a disclinated graphene in the presence of an external magnetic field. Within a continuum approach, the problem is mathematically modeled by the definition of a special vector potential containing all the information about the topology and the interacting fields. The presence of disclination is introduced by a term in the Dirac equation that translates the appearance of a phase associated with the transport of the spinor around the apex of the cone. We solve exactly the Dirac equation for this problem and the eigenvalues are obtained. We observe the influence of the disclination on the spectrum of energy and the allowed values of magnetic field.     

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 and band structure—A unified treatment through the quantum Hamilton-Jacobi approach

We analyze the Scarf potential, which exhibits both discrete energy bound states and energy bands, through the quantum Hamilton-Jacobi approach. The singularity structure and the boundary conditions in the above approach, naturally isolate the bound and periodic states, once the problem is mapped to the zero energy sector of another quasi-exactly solvable quantum problem. The energy eigenvalues are obtained without having to solve for the corresponding eigenfunctions explicitly. We also demonstrate how to find the eigenfunctions through this method.     

量子围栏中的表面电子态

将量子围栏作为二维无限深势阱来处理,用定态Schr dinger方程求出其波函数,并对围栏中的表面电子状态进行了讨论,最后在这一理论模型基础之上用MATLAB 6.1对模型计算结果进行了模拟和讨论,较好地解释了量子围栏中的表面电子所展现出的波动现象.     

Bound states in continuum of complex potentials generated by supersymmetric quantum mechanics

It is shown that bound states in continuum can be generated by applying supersymmetric quantum mechanics to real potentials in such a way that the transformed potential becomes complex. Three cases of the initial potential are considered in more detail: flat potential, step potential and rectangular quantum well. The conditions are found for the existence of bound state in continuum in these cases, as well as the expressions for the wavefunction of this state and the corresponding complex potential in analytic form.