Dynamics of Vortex Electrons in a Uniform Magnetic Field Across Nonrelativistic and Relativistic Regimes
The dynamics of a vortex electron in a transverse uniform magnetic field involves not only the cyclotron motion of the wave packet center but also the evolution of its internal wavefunction structure. To study this process, we develop a quantum framework and investigate the dynamics of vortex electrons in both the nonrelativistic and relativistic regimes. A discrete Bessel-Gaussian initial wave packet is expanded in the basis of Dirac eigenstates to obtain the time-dependent wavefunction and to analyze its spatiotemporal evolution. In the nonrelativistic regime, the results deviate significantly from the rigid point-dipole model, as the intrinsic kinetic orbital angular momentum exhibits dynamics more complex than simple Larmor precession, owing to the nonstationary internal current distribution of the wave packet. In the relativistic regime, the nonlinear dependence of the energy levels on the quantum numbers destroys the equal spacing of the spectrum. Consequently, the relative phases among the eigenstate components of the wave packet evolve nonuniformly, resulting in wave-packet spreading and deformation, accompanied by modified intrinsic orbital angular momentum dynamics. We introduce a dimensionless parameter to quantify this relativistic dephasing, providing an approximate criterion for selecting physical parameters and evolution times to mitigate the resulting wave-packet distortion. These results clarify the limitations of the rigid point-dipole model, highlight the essential role of internal wavefunction structure, and provide theoretical guidance for understanding and manipulating relativistic vortex electrons.