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Abdulaziz D. Alhaidari

Publications and source records attributed to Abdulaziz D. Alhaidari.

9 recordsLinked to original sources
arXiv2023

Electron trapping in graphene quantum dots with magnetic flux

It is known that the appearance of Klein tunneling in graphene makes it hard to keep or localize electrons in a graphene-based quantum dot (GQD). However, a magnetic field can be used to temporarily confine an electron that is traveling into a GQD. The electronic states investigated here are resonances with a finite trapping time, also referred to as quasi-bound states. By subjecting the GDQ to a magnetic flux, we study the scattering phenomenon and the Aharonov-Bohm effect on the lifetime of quasi-bound states existing in a GQD. We demonstrate that the trapping time increases with the magnetic flux sustaining the trapped states for a long time even after the flux is turned off. Furthermore, we discover that the probability density within the GQD is also clearly improved. We demonstrate that the trapping time of an electron inside a GQD can be successfully extended by adjusting the magnetic flux parameters.

cond-mat.mes-hall↗
arXiv2020

J-matrix method of scattering for inverse-square singular potential with supercritical coupling I. Theory

The J-matrix method of scattering was developed to handle regular short-range potentials with applications in atomic, nuclear and molecular physics. Its accuracy, stability, and convergence properties compare favorably with other successful scattering methods. It is an algebraic method, which is built on the utilization of orthogonal polynomials that satisfy three-term recursion relations and on the manipulation of tridiagonal matrices. Recently, we extended the method to the treatment of 1/r^2 singular short-range potentials but confined ourselves to the sub-critical coupling regime where the coupling parameter strength of the 1/r^2 singularity is greater than -1/8. In this work, we expand our study to include the supercritical coupling in which the coupling parameter strength is less than -1/8. However, to accomplish that we had to extend the formulation of the method to objects that satisfy five-term recursion relations and matrices that are penta-diagonal. It is remarkable that we could develop the theory without regularization or self-adjoint extension, which are normally needed in the treatment of such highly singular potentials. Nonetheless, we had to pay the price by extending the formulation of the method into this larger representation and by coping with slower than usual convergence. In a follow-up study, we intend to apply the method to obtain scattering information for realistic potential models.

quant-ph↗
arXiv2020

Construction of potential functions associated with a given energy spectrum -- An inverse problem. II

We continue our solution of the inverse problem started by the first author in [Int. J. Mod. Phys. A 35, xxxx (2020), in production]. Additional potential functions for exactly solvable problems that correspond to the same energy spectrum formula but for different energy polynomials and bases are found. In this work, we obtain a class of potential functions associated with the Wilson polynomial and "Jacobi basis".

quant-ph↗
arXiv2013

Graphene Nanoribbon in Sharply Localized Magnetic Fields

We study the effect of a sharply localized magnetic field on the electron transport in a strip (ribbon) of graphene sheet, which allows to give results for the transmission and reflection probability through magnetic barriers. The magnetic field is taken as a single and double delta type localized functions, which are treated later as the zero width limit of gaussian fields. For both field configurations, we evaluate analytically and numerically their transmission and reflection coefficients. The possibility of spacial confinement due to the inhomogeneous field configuration is also investigated.

cond-mat.mes-hall↗
arXiv2012

Extension and exact realization of the Heller's derivative rule

The accuracy of the Heller's derivative rule to calculate the numerical weights associated with discretized energy spectrum is enhanced by Broad's extension which adds (N-1) more interpolating points to the original N points. The extension scheme is then used to show how to realize the rule without any approximation.

math-ph↗
arXiv2012

Confined Dirac Particles in Constant and Tilted Magnetic Field

We study the confinement of charged Dirac particles in 3+1 space-time due to the presence of a constant and tilted magnetic field. We focus on the nature of the solutions of the Dirac equation and on how they depend on the choice of vector potential that gives rise to the magnetic field. In particular, we select a "Landau gauge" such that the momentum is conserved along the direction of the vector potential yielding spinor wavefunctions, which are localized in the plane containing the magnetic field and normal to the vector potential. These wave functions are expressed in terms of the Hermite polynomials. We point out the relevance of these findings to the relativistic quantum Hall effect and compare with the results obtained for a constant magnetic field normal to the plane in 2+1 dimensions.

hep-th↗
arXiv2009

Confined Dirac Fermions in a Constant Magnetic Field

We obtain an exact solution of the Dirac equation in (2+1)-dimensions in the presence of a constant magnetic field normal to the plane together with a two-dimensional Dirac-oscillator potential coupling. The solution space consists of a positive and negative energy solution, each of which splits into two disconnected subspaces depending on the sign of an azimuthal quantum number, k = 0, \pm 1, \pm 2,... and whether the cyclotron frequency is larger or smaller than the oscillator frequency. The spinor wavefunction is written in terms of the associated Laguerre polynomials. For negative k, the relativistic energy spectrum is infinitely degenerate due to the fact that it is independent of k. We compare our results with already published work and point out the relevance of these findings to a systematic formulation of the relativistic quantum Hall effect in a confining potential.

hep-th↗