Off-Axis Vortices Retain Spin Despite Magnetic Field Shifts

Researchers at Sun Yat-Sen University have discovered that electrons can maintain their orbital angular momentum (OAM) even when displaced from the center of magnetic fields. The work identifies an SU(1,1) invariant that explains how these off-axis electron vortices retain this crucial property, challenging the understanding that rotational symmetry is required for stable behavior. The researchers suggest this conservation may explain why it has remained unnoticed. First-principles simulations, utilizing a Glaser lens, successfully confirmed the predicted robustness of these off-axis vortices, demonstrating a reliable transport mechanism in axisymmetric nonuniform magnetic fields.

SU(1,1) Invariant Conserves Off-Axis Orbital Angular Momentum

Researchers at Sun Yat-Sen University identified an SU(1,1) dynamical invariant responsible for this conservation, revealing a previously unknown mechanism governing electron behavior in axisymmetric, yet nonuniform, magnetic fields. This discovery is not merely an observation of stability, but a fundamental principle operating outside the usual framework of symmetry-based conservation laws. The team’s work demonstrates that the intrinsic orbital angular momentum (OAM) of these off-axis electron vortices remains constant during propagation, despite lacking the protective symmetry present in on-axis systems. Rotational symmetry protects the topological charge of on-axis electron vortices, but not of off-axis vortices. The researchers state in their published work that “the intrinsic OAM of an off-axis vortex is exactly conserved during propagation through axisymmetric nonuniform magnetic fields, despite the absence of centroid-frame symmetry protection.”

This conservation, they explain, arises from a combination of axial symmetry, which fixes the total canonical orbital angular momentum, and the newly identified SU(1,1) invariant, which prevents any transfer of angular momentum into the intrinsic component. To validate their theoretical predictions, the researchers performed first-principles simulations of an off-axis electron vortex traveling through a Glaser lens. These simulations, solving the three-dimensional Schrödinger equation, confirmed the robustness of the vortices, preserving both their structure and intrinsic orbital angular momentum (OAM) over considerable distances and with significant transverse misalignment. The simulations even accounted for field gradients steeper than those typically found in experiments, further demonstrating the reliability of this transport mechanism in practical electron-optical systems.