On the electron vortex beam wavefunction within a crystal

Electron vortex beams are distorted by scattering within a crystal, so that the wavefunction can effectively be decomposed into many vortex components. Using a Bloch wave approach equations are derived for vortex beam decomposition at any given depth and with respect to any frame of reference. In the kinematic limit (small specimen thickness) scattering largely takes place at the neighbouring atom columns with a local phase change of pi/2 rad. When viewed along the beam propagation direction only one vortex component is present at the specimen entrance surface (i.e. the 'free space' vortex in vacuum), but at larger depths the probe is in a mixed state due to Bragg scattering. Simulations show that there is no direct correlation between vortex components and the pendellosung, i.e. at a given depth probes with relatively constant < L-z > can be in a more mixed state compared to those with more rapidly varying < L-z > This suggests that minimising oscillations in the < L-z > pendellosung by probe channelling is not the only criterion for generating a strong electron energy loss magnetic circular dichroism (EMCD) signal. (C) 2015 Elsevier B.V. All rights reserved.