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A theoretical model for quantum nanostructures electronic wave functions, magnetic field effects
Physica E: Low-dimensional Systems and Nanostructures, 2005
Analytical solutions of electronic wave functions in symmetric quantum ring (QR), quantum wire (QWR) and quantum dots (QD) structures are given using a parabolic coordinates system. The solutions for low-energy states are combinations of Bessel functions. The density of states of perfect 1D QR and QWR are shown to be equivalent. The continuous evolution from a 0D QD to a perfect 1D QR can be precisely described. The sharp variation of electronic properties, related to the build up of a potential energy barrier at the early stage of the QR formation, is studied analytically. Paramagnetic and diamagnetic couplings to a magnetic field are computed for QR and QD. It is shown theoretically that magnetic field induces an oscillation of the magnetization in QR. r
Aharonov-Bohm Effect in Quantum Nanocups
ITECKNE, 2014
The Aharonov-Bohm effect had been studied in semiconductor ring system and type II quantum dots, different authors had considered the asymmetric effect in the shape of the ring and the effect on Aharonov-Bohm oscillation due to impurities in the structure. In this report is considering the effect of a magnetic field applied on the electron energy inside in a quantum nanocup. The energy is calculated using a vibrational procedure in the effective mass framework. The results show the influence of the shape of a nanocup on the electron energy and smooth oscillation in the ground state energy as a function of the magnetic field.
Quantum ring in a rotating frame in the presence of a topological defect
Physics Letters A, 2015
In this contribution, we study the effects caused by rotation of an electron/hole in the presence of a screw dislocation confined in a quantum ring potential, within a quantum dynamics. The Tan-Inkson potential is used to model the confinement of the particle in two-dimensional quantum ring. We suppose that the quantum ring is placed in the presence of an external uniform magnetic field and an Aharonov-Bohm flux in the center of the system, and that the frame rotates around the z-axis. The Schrödinger equation is solved and the eigenfunctions and energy eigenvalues are exactly obtained for this configuration. The influence of the dislocation and the rotation on both the persistent current and magnetization is also studied.
Optical and electronic properties of a two-dimensional quantum ring under rotating effects
arXiv (Cornell University), 2023
This work presents a study on the nonrelativistic quantum motion of a charged particle in a rotating frame, considering the Aharonov-Bohm effect and a uniform magnetic field. We derive the equation of motion and the corresponding radial equation to describe the system. The Schrödinger equation with minimal coupling incorporates rotation effects by substituting the momentum operator with an effective four-potential. Additionally, a radial potential term, dependent on the average radius of the ring, is introduced. The analysis is restricted to motion in a two-dimensional plane, neglecting the degree of freedom in the z-direction. By solving the radial equation, we determine the eigenvalues and eigenfunctions, allowing for an explicit expression of the energy. The probability distribution is analyzed for varying rotating parameter values, revealing a shift of the distribution as the rotation changes, resulting in a centrifugal effect and occupation of the ring's edges. Furthermore, numerical analysis demonstrates the significant rotational effects on energy levels and optical properties, including optical absorption and refractive coefficients.
Quantum states on spheres in the presence of magnetic fields
2019
The study of quantum states on the surface of various two-dimensional geometries in the presence of strong magnetic fields has proven vital to the theoretical understanding of the quantum Hall effect. In particular, Haldane’s seminal study of quantum states on the surface of a compact geometry, the sphere, in the presence of a monopole magnetic field, was key to developing an early understanding of the fractional quantum Hall effect. Most of the numerous studies undertaken of similar systems since then have been limited to cases in which the magnetic fields are everywhere constant and perpendicular to the surface on which the charged particles are confined. In this thesis, we study two novel variations of Haldane’s spherical monopole system: the ‘squashed sphere’ in the presence of a monopole-like magnetic field, and the sphere in the presence of a dipole magnetic field. In both cases the magnetic field is neither perpendicular nor constant with respect to the surface on which the c...
A cylindrical -potential in external magnetic fields: a model for semiconductor nanostructures
Journal of Physics: Condensed Matter, 1996
A semiconductor nanostructure represented by the cylindrical electrostatic δpotential subjected to magnetic fields is considered theoretically. The possibility of particle penetration into the region outside the ring for a finite opacity leads to modification of the energy spectrum and the associated azimuthal currents compared to the results for the quantum ring. In particular, when the Aharonov-Bohm whisker is introduced at the origin the currents do not tend to zero in the limit of vanishing magnetic flux. This is attributed to the change of the topology of the structure after introducing the non-zero Aharonov-Bohm flux. This feature diminishes when more realistic distributions of the magnetic field are considered. For uniform magnetic fields anticrossings of the energy levels are observed as a function of the magnetic index and their role in determining the quantum currents is investigated for a wide range of the potential strength. Similarities and differences between the rectangular and cylindrical geometry are discussed.
Physica E: Low-dimensional Systems and Nanostructures, 2004
The evolution of non-stationary localized states jCðt ¼ 0Þi is investigated in two-dimensional tight binding systems of N potential wells with and without a homogeneous field perpendicular to the plane. Most results are presented in analytical form, what is almost imperative if the patterns are as complex as for rings in a magnetic field, where the qualitatively different features arise depending on rational or irrational numbers. The systems considered comprise finite linear chains ðN ¼ 2; 3Þ, finite rings (N ¼ 3-6), infinite chains, finite rings (N ¼ 3-6) in a magnetic field, and rings with leads attached to each ring site. The position of the particle at time t is described by the projection of the wave function P m ðtÞ ¼ jhmjCðtÞij 2 onto the localized basis function at site m. For finite chains and rings with N ¼ 3; 4; 6 the time evolution is periodic, whereas it is non-periodic for N ¼ 5 and N greater then 6. Rings in a magnetic field show a rich spectrum of different features depending on N and the number of flux quanta through the ring, including periodic oscillation and rotation of the charge as well as non-periodic charge fluctuations. r
2010
The electronic structure of the conduction and valence bands of a quantum ring containing a layer inside the ring opening is modeled. This structure (nanocup) consists of a GaAs nanodisk (the cup's bottom) and a GaAs nanoring (the cup's rim) which encircles the disk. The whole system is embedded in an (Al,Ga)As matrix, and its shape resembles realistic ring structures grown by the droplet epitaxy technique. The conduction-band states in the structure are modeled by the single-band effective-mass theory, while the 4-band Luttinger-Kohn model is adopted to compute the valence-band states. We analyze how the electronic structure of the nanocup evolves from the one of a quantum ring when the size of either the nanodisk or the nanoring is changed. For that purpose, (1) the width of the ring, (2) the disk radius, and (3) the disk height are separately varied. For dimensions typical for experimentally realized structures, we find that the electron wavefunctions are mainly localized inside the ring, even when the thickness of the inner layer is 90% of the ring thickness. These calculations indicate that topological phenomena, like the excitonic Aharonov-Bohm effect, are negligibly affected by the presence of the layer inside the ring.
Quantum rings of arbitrary shape and non-uniform width in a threading magnetic field
Physical Review B, 2008
The electronic states of quantum rings with centerlines of arbitrary shape and non-uniform width in a threading magnetic field are calculated. The solutions of the Schrödinger equation with Dirichlet boundary conditions are obtained by a variational separation of variables in curvilinear coordinates. We obtain a width profile that compensates for the main effects of the curvature variations in the centerline. Numerical results are shown for circular, elliptical, and limaçon-shaped quantum rings. We also show that smooth and tiny variations in the width may strongly affect the Aharonov-Bohm oscillations.