Electrodynamics of swift-electron momentum transfer to a large spherical nanoparticle

TL;DR

This paper develops a causal, efficient electrodynamic framework to accurately compute linear momentum transfer from swift electrons to large spherical nanoparticles, clarifying previous conflicting predictions and establishing benchmarks for nanoscale electron-beam manipulation.

Contribution

The authors derive analytical expressions and a numerical framework for causal momentum transfer calculations, resolving prior issues with non-causal models and demonstrating net attractive forces.

Findings

Net transverse momentum transfer remains attractive for all studied nanoparticles.

Causality and full multipolar convergence are crucial for accurate predictions.

Material-specific resonances influence the spectral density of momentum transfer.

Abstract

Swift electrons from highly focused beams produced in aberration-corrected scanning transmission electron microscopes offer a powerful route for probing and manipulating matter at the nanoscale. Although linear momentum transfer from swift electrons to nanoparticles has been investigated theoretically and experimentally, subsequent analyzes revealed that several earlier predictions relied on non-causal dielectric functions or insufficient numerical convergence, leading to spurious sign reversals in the transferred momentum. Here, we derive analytical expressions and develop a numerically efficient electrodynamic framework to compute the linear momentum transferred from a swift electron to an isolated spherical nanoparticle described by a fully causal, local dielectric response. We apply our framework to large nanoparticles with 50 nm radius and explicitly resolve the spectral density of linear momentum transfer across the full frequency domain. Using causal dielectric functions for aluminum and bismuth, we analyze the role of electron velocity, impact parameter, and material-specific resonances. We find that, when causality and full multipolar convergence are enforced, the net transverse linear momentum transferred to spherical nanoparticles remains attractive toward the electron trajectory for all nanoparticles considered, despite the presence of material-dependent sign changes in individual electric and magnetic contributions. These results contrast with earlier theoretical predictions of net repulsive behavior and indicate that additional physical mechanisms beyond the present isolated, local description are required to account for experimentally observed repulsion. Our work establishes a robust reference framework for momentum transfer calculations and provides quantitative benchmarks relevant for electron-beam-based nanoscale manipulation.