Dynamical Diffraction Theory for Wave Packet Propagation in Deformed Crystals

TL;DR

This paper develops a dynamical diffraction theory for x-ray wave packets in deformed crystals, incorporating Berry phase effects, and predicts enhanced trajectory shifts near Bragg conditions.

Contribution

It introduces a new set of equations of motion for x-ray wave packets that include Berry phase corrections and accounts for crystal deformation effects.

Findings

Wave packet trajectory shifts are enhanced near Bragg conditions.

The theory predicts a measurable displacement due to crystal deformation.

Comparison with conventional theory shows additional Berry phase effects.

Abstract

We develop a theory for the trajectory of an x ray in the presence of a crystal deformation. A set of equations of motion for an x-ray wave packet including the dynamical diffraction is derived, taking into account the Berry phase as a correction to geometrical optics. The trajectory of the wave packet has a shift of the center position due to a crystal deformation. Remarkably, in the vicinity of the Bragg condition, the shift is enhanced by a factor $\omega /\Delta \omega$ ($\omega$: frequency of an x ray, $\Delta\omega$: gap frequency induced by the Bragg reflection). Comparison with the conventional dynamical diffraction theory is also made.