Tennis-racket instability of twisted electrons

TL;DR

This paper reveals how a weak nonlinear magnetic edge causes a tennis-racket instability in twisted electrons, leading to recurrent pseudospin reversals and profile conversions observable in electron microscopes.

Contribution

It introduces a Maxwell-consistent model showing how a weak nonlinear edge induces a tennis-racket instability in twisted electron pseudospin dynamics.

Findings

Recurrent reversals of pseudospin projection observed.

Profile conversions between vortex and multi-lobed states.

Instability regime accessible with standard electron microscope correctors.

Abstract

We demonstrate that a weak nonlinear magnetic entrance edge induces a tennis-racket (Dzhanibekov) instability in the shell-resolved orbital pseudospin dynamics of twisted electrons propagating in a nominally uniform solenoidal field. Starting from a Maxwell-consistent thin-edge extension of the entrance field, we derive an effective fixed-shell Hamiltonian in which linear Schwinger pseudospin precession acquires an anisotropic quadratic correction. In the symmetric aligned limit, an exact linear eigenstate (a Laguerre-Gaussian vortex state) becomes a hyperbolic fixed point of the large-shell dynamics, producing recurrent reversals of the mean pseudospin projection. These reversals appear in real space as repeated conversions of the transverse profile between Laguerre-Gaussian vortex and Hermite-Gaussian multi-lobed states. The unavoidable Lewis-Ermakov breathing of realistic wave packets does not generate a separate mechanism; it naturally modulates the nonlinear strength and sets the growth time scale. Microscope-scale estimates show that the required regime is accessible with standard octupole correctors in a transmission electron microscope.