Dynamic scattering of electron vortex beams – A Bloch wave analysis

Two important applications of electron vortex beams are in electron magnetic chiral dichroism (EMCD) measurements and nanoparticle manipulation. In both cases orbital angular momentum (〈Lz〉) transfer between the vortex beam and the specimen due to dynamic scattering is critical. In general the 〈Lz〉 pendellösung consists of short and long wavelength oscillations. The former is due to interference between the tightly bound 1s and more dispersive non-1s Bloch states, while the latter is due to interference between the non-1s states. For EMCD experiments with ±ħ angular momentum beams, momentum transfer can be minimised by selecting the appropriate aperture size, so that the probe wavefunction approximately matches that of the 2p-type Bloch states. For manipulating nanoparticles with large angular momentum beams small apertures are required to excite the 1s state and thereby enhance the short wavelength oscillations in 〈Lz〉. This enables efficient momentum transfer to the specimen, provided the nanoparticle dimension corresponds to a minimum in the 〈Lz〉 pendellösung.