Quantum interaction of sub-relativistic aloof electrons with mesoscopic samples

TL;DR

This paper explores the quantum effects in the interaction between sub-relativistic electrons and mesoscopic samples, revealing significant quantum features that challenge classical models, especially at lower energies and larger interaction lengths.

Contribution

The authors develop a macroscopic quantum electrodynamics framework to analytically include recoil effects in electron energy loss calculations, extending beyond classical point-charge models.

Findings

Quantum interaction effects become stronger with increased interaction length and decreased electron energy.

Significant energy loss probabilities occur at higher energy losses and larger impact parameters, contrary to classical expectations.

Classical models fail to capture the quantum features observed in the aloof electron-sample interactions.

Abstract

Relativistic electrons experience very slight wave packet distortion and negligible momentum recoil when interacting with nanometer-sized samples, as a consequence of the ultra-short interaction time. Accordingly, modeling fast electrons as classical point-charges provides extremely accurate theoretical predictions of energy-loss spectra. Here we investigate the aloof interaction of nanometer-sized electron beams of few keV with micron-sized samples, a regime where the classical description generally fails due to significant wavefunction broadening and momentum recoil. To cope with these effects, we use macroscopic quantum electrodynamics to analytically derive a generalized expression for the electron energy loss probability which accounts for recoil. Quantum features of the interaction are shown to get dramatically strong as the interaction length is increased and/or the electron kinetic energy is decreased. Moreover, relatively large values of the energy loss probability are found at higher energy losses and larger impact parameters, a marked quantum effect which is classically forbidden by the evanescent profile of the field produced by a moving point-charge.