Electron decoherence in cylindrical holes and circular apertures
Abstract
The coherence of free electrons sets fundamental limits on the resolution and contrast of phase-sensitive electron microscopy because coherence is lost whenever the electron leaves a distinguishing excitation in its environment. We develop a quantitative theory of fast-electron decoherence in two canonical geometries: a cylindrical hole drilled through a realistic metal and a circular aperture in a thin perfectly conducting film. By combining an electromagnetic Green-tensor formulation with the fluctuation--dissipation theorem while fully retaining retardation, we obtain the decoherence probability and elastic phase as functions of the electron trajectory, temperature, and material response. For the cylindrical hole, we obtain a closed-form, azimuthally resolved expression that separates the dependences on path position, temperature, and conductivity. In the high-conductivity and high-temperature limits, this result reduces to a universal expression that is linear in temperature and independent of both conductivity and electron velocity. For the circular aperture, which we solve using a cylindrical-wave modal expansion, the energy-loss probability diverges as 1/ω at low frequency, whereas the decoherence probability remains finite and reaches a maximum when the aperture radius is comparable to the relevant electromagnetic wavelength. Because the interaction is spatially localized, aperture-induced decoherence is generally weaker than that produced by a cylindrical hole, except for sufficiently large apertures at high temperature. Finally, we show that, for sufficiently large holes, decoherence can dominate the spatial broadening of a focused electron probe and must therefore be incorporated into the design of coherent electron-beam instruments.
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BibTeX
@misc{velasco2026electron,
title = {{Electron decoherence in cylindrical holes and circular apertures}},
author = {Cruz I. Velasco and F. Javier Garc\'ıa de Abajo},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.35498},
eprint = {2609.35498},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.35498},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Electron decoherence in cylindrical holes and circular apertures
AU - Cruz I. Velasco
AU - F. Javier Garc\'ıa de Abajo
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.35498
UR - https://arxiv.org/abs/2609.35498
AB - The coherence of free electrons sets fundamental limits on the resolution and contrast of phase-sensitive electron microscopy because coherence is lost whenever the electron leaves a distinguishing excitation in its environment. We develop a quantitative theory of fast-electron decoherence in two canonical geometries: a cylindrical hole drilled through a realistic metal and a circular aperture in a thin perfectly conducting film. By combining an electromagnetic Green-tensor formulation with the fluctuation--dissipation theorem while fully retaining retardation, we obtain the decoherence probability and elastic phase as functions of the electron trajectory, temperature, and material response. For the cylindrical hole, we obtain a closed-form, azimuthally resolved expression that separates the dependences on path position, temperature, and conductivity. In the high-conductivity and high-temperature limits, this result reduces to a universal expression that is linear in temperature and independent of both conductivity and electron velocity. For the circular aperture, which we solve using a cylindrical-wave modal expansion, the energy-loss probability diverges as 1/ω at low frequency, whereas the decoherence probability remains finite and reaches a maximum when the aperture radius is comparable to the relevant electromagnetic wavelength. Because the interaction is spatially localized, aperture-induced decoherence is generally weaker than that produced by a cylindrical hole, except for sufficiently large apertures at high temperature. Finally, we show that, for sufficiently large holes, decoherence can dominate the spatial broadening of a focused electron probe and must therefore be incorporated into the design of coherent electron-beam instruments.
ER -