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arXiv:2607.22315

Robustness of Off-Axis Electron Vortices in Nonuniform Magnetic Fields

Hui-Dong Huang, Qi Meng, Zhi-Bin Wang, Liang Lu, Jian Chen, Li-Ping Zou

physics.acc-phphysics.plasm-phquant-phSubmitted Jul 24, 2026• Announced Jul 27, 2026
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Abstract

Rotational symmetry protects the topological charge of on-axis electron vortices but not of off-axis vortices. We identify an additional SU(1,1) dynamical invariant that guarantees conservation of their intrinsic orbital angular momentum within the near-axis approximation. First-principles simulations of an off-axis electron vortex traversing a Glaser lens confirm this prediction, establishing a robust transport mechanism in axisymmetric nonuniform magnetic fields.

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Rotational symmetry protects the topological charge of on-axis electron vortices but not of off-axis vortices. We identify an additional SU(1,1) dynamical invariant that guarantees conservation of their intrinsic orbital angular momentum within the near-axis approximation. First-principles simulations of an off-axis electron vortex traversing a Glaser lens confirm this prediction, establishing a robust transport mechanism in axisymmetric nonuniform magnetic fields.
We consider the orbital angular momentum of a free electron vortex moving in a uniform magnetic field. We identify three contributions to this angular momentum: the canonical orbital angular momentum associated with the vortex, the angular momentum of the cyclotron orbit of the wavefunction, and a diamagnetic angular momentum. The cyclotron and diamagnetic angular momenta are found to be separable according to the parallel axis theorem. This means that rotations can occur with respect to two or more axes simultaneously, which can be observed with superpositions of vortex states.
In this paper we present a gauge-invariant formalism for describing the spin and orbital angular momenta of scalar and vector optical vortices. The correction term, arising from consistent incorporation of the transverse vector potential's nonlocality, restores gauge invariance and makes it possible to separate the total angular momentum into spin and orbital components. We propose a method for calculating the orbital and spin angular momenta of multimode vector vortex fields and show that the orbital angular momentum of such beams contains two qualitatively different components. The polarization-independent contribution to the orbital angular momentum is related to the topological charge that determines the order of the phase singularity, while the polarization-dependent one is proportional to the helical topological charge that determines the spatial inhomogeneity of the polarization. We also discuss the quantization procedure for fields with spatially inhomogeneous polarization in terms of modes with a helical topological charge, and examine the limits of applicability of the proposed formalism.
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We revisit ground states of spinor Bose-Einstein condensates with a Rashba spin-orbit coupling, and find that various types of vortices show up without rotation as a direct consequence of spontaneous symmetry breaking into a combined gauge, spin, and space rotation symmetry. The combined symmetry also determines the vortex-core spin state at the rotating center. For the continuous combined symmetry, the spin rotates by $2\ensuremath{\pi}$ around the rotating axis, whereas for the discrete combined symmetry, we further need 2F2F2F quantum numbers to determine how much the spin rotates for the spin-FFF system. For lattice phases we find that in the ground state the topological charge for each unit cell vanishes. However, we find two types of highly symmetric lattices with nontrivial topological charges for the spin-12\frac{1}{2}21​ system based on the symmetry classification, and show that they are Skyrmion crystals.