Related papers: Foldy-Wouthuysen transformation and multiwave states of a graphene electron in external fields and free (2+1)-space

Foldy-Wouthuysen transformation and multiwave states of a graphene electron in external fields and free (2+1)-space

URL: http://arxiv.org/abs/2305.11879v1
Date: Sun, 7 May 2023 17:03:00 GMT
Title: Foldy-Wouthuysen transformation and multiwave states of a graphene electron in external fields and free (2+1)-space
Authors: Alexander J. Silenko
Abstract summary: Graphene electrons in a static electric field can exist in the multiwave Hermite-Gauss states defining non-spreading coherent beams. It is proven that the Hermite-Gauss beams exist even in the free space.
Score: 91.3755431537592
License: http://creativecommons.org/licenses/by/4.0/
Abstract: The relativistic Foldy-Wouthuysen transformation is used for an advanced description of planar graphene electrons in external fields and free (2+1)-space. It is shown that the initial Dirac equation should contain usual Dirac matrices but not the Pauli ones. The spin of graphene electrons is not the isotopic spin and takes the values $\pm1/2$. The exact Foldy-Wouthuysen Hamiltonian of a graphene electron in uniform and nonuniform magnetic fields is derived. The exact energy spectrum agreeing with experimental data and exact Foldy-Wouthuysen wave eigenfunctions are obtained. These eigenfunctions describe multiwave (structured) states in (2+1)-space. It is proven that the Hermite-Gauss beams exist even in the free space. In the multiwave Hermite-Gauss states, graphene electrons acquire nonzero effective masses dependent on a quantum number and move with group velocities which are less than the Fermi velocity. Graphene electrons in a static electric field also can exist in the multiwave Hermite-Gauss states defining non-spreading coherent beams. These beams can be accelerated and decelerated.

Related papers

Spin Current Density Functional Theory of the Quantum Spin-Hall Phase [59.50307752165016]
We apply the spin current density functional theory to the quantum spin-Hall phase. We show that the explicit account of spin currents in the electron-electron potential of the SCDFT is key to the appearance of a Dirac cone.
arXiv Detail & Related papers (2022-08-29T20:46:26Z)
Electron Wave Spin in a Quantum Well [0.0]
We show that a stable circulating total current density exists inside the well with a donut shaped topography. A spin value is modified by the confining geometry of the well. A free electron Gaussian wavepacket is unstable and experiences quick decoherence.
arXiv Detail & Related papers (2022-03-17T16:50:36Z)
New Class of Landau Levels and Hall Phases in a 2D Electron Gas Subject to an Inhomogeneous Magnetic Field: An Analytic Solution [0.0]
Solution provides access to many properties of a two-dimensional, non-interacting, electron gas in the thermodynamic limit. Radially distorted Landau levels can be identified as well as magnetic field induced density and current oscillations close to the magnetic impurity.
arXiv Detail & Related papers (2022-01-13T16:52:02Z)
Band strutures of hybrid graphene quantum dots with magnetic flux [0.0]
We study the band structures of hybrid graphene quantum dots subject to a magnetic flux and electrostatic potential. For the valley $K'$, it is found that the magnetic flux strongly acts by decreasing the gap and shifting energy levels away from zero radius with some oscillations.
arXiv Detail & Related papers (2021-07-30T12:04:13Z)
Relativistic aspects of orbital and magnetic anisotropies in the chemical bonding and structure of lanthanide molecules [60.17174832243075]
We study the electronic and ro-vibrational states of heavy homonuclear lanthanide Er2 and Tm2 molecules by applying state-of-the-art relativistic methods. We were able to obtain reliable spin-orbit and correlation-induced splittings between the 91 Er2 and 36 Tm2 electronic potentials dissociating to two ground-state atoms.
arXiv Detail & Related papers (2021-07-06T15:34:00Z)
Motion-induced radiation due to an atom in the presence of a graphene plane [62.997667081978825]
We study the motion-induced radiation due to the non-relativistic motion of an atom in the presence of a static graphene plate. We show that the effect of the plate is to increase the probability of emission when the atom is near the plate and oscillates along a direction perpendicular to it.
arXiv Detail & Related papers (2021-04-15T14:15:23Z)
Energy spectrum of massive Dirac particles in gapped graphene with Morse potential [0.0]
We study the massive Dirac equation with the presence of the Morse potential in polar coordinate. The Dirac Hamiltonian is written as two second-order differential equations in terms of two spinor wavefunctions. We investigate the graphene band structure by a linear dispersion relation which creates an energy gap in the Dirac points called gapped graphene.
arXiv Detail & Related papers (2021-04-14T09:26:56Z)
A photon model based upon chaos produced by static, Schwinger-level electric field nonlinearities that satisfies all first-order properties [0.0]
We postulate that Schwinger's threshold for a dynamic electric field intensity to induce nonlinearity is a special case. Within an atom they support inter-state energy transfers and intra-state chaotic mixing of time-varying fields. The photon charge-field ensemble, which we show is localizable, is thermodynamically closed and possesses all first-order photon properties.
arXiv Detail & Related papers (2020-08-26T15:14:02Z)
Electrically tuned hyperfine spectrum in neutral Tb(II)(Cp$^{\rm{iPr5}}$)$_2$ single-molecule magnet [64.10537606150362]
Both molecular electronic and nuclear spin levels can be used as qubits. In solid state systems with dopants, an electric field was shown to effectively change the spacing between the nuclear spin qubit levels. This hyperfine Stark effect may be useful for applications of molecular nuclear spins for quantum computing.
arXiv Detail & Related papers (2020-07-31T01:48:57Z)
General quantum-mechanical solution for twisted electrons in a uniform magnetic field [68.8204255655161]
A theory of twisted (and other structured) paraxial electrons in a uniform magnetic field is developed. The observable effect of a different behavior of relativistic Laguerre-Gauss beams with opposite directions of the orbital angular momentum penetrating from the free space into a magnetic field is predicted.
arXiv Detail & Related papers (2020-05-13T16:35:10Z)

This list is automatically generated from the titles and abstracts of the papers in this site.