High-Angular Splitting Electron Vortex Beams Generated by Topological Defects

Abstract

Wavefront shaping of transmitted electrons has attracted lots of attentions due to its wide application in materials science and biology. Particularly electron vortex beam carrying an orbital angular momentum can potentially detect magnetic signals at the atomic resolution by theoretical calculations [1,2]. Up to now there are many approaches to realize the vortex beam with desired topological charges via the predesigned phase plate [3][4][5][6]. In 2010, Verbeeck and his colleagues used pitch-fork aperture made in a thinned Pt foil to generate vortex beam [4]. Although the current technology such as focused ion beam and electron beam lithography enables us to fabricate the desired phase plate, e.g. the artificial "Y"-like nanofabricated hologram, for generating electron vortex beams, the spacing in the phase plate can only reach at the nanometer scale due to the limited processing precision. It is challenging to make highangular splitting of electron vortex beams Fortunately, topological defects in solid-state materials offer a feasible route for the fabrication of phase plates which brings on the wave function of electrons being converted from plane wave to electron vortex by breaking the translational symmetry. We performed a series of experiment on a NiO sample epitaxial grown on a SrTiO3 substrate to demonstrated how defects bring about the interaction between high-energy electron beam and topological orders [7].In the case of edge dislocations, an extra plane causes a 2π phase-winding topological defect which leads to the same topological pattern as the "Y"-like holograms in a three-beam condition. This equivalency enables us to use it as a "Y"-like hologram. When a plane wave of electron passing through the "Y"-like hologram, it can generate a series of electron vortex beams with increasing order of topological charge. We formed a coherent electron nanobeam in a scanning transmission electron microscope and recorded the far-field transmitted patterns as the beam steps through the edge dislocation core of NiO. Interestingly, the amplitude patterns of the Bragg disks evolve in a similar manner to the evolution of an annular solar eclipse. More importantly, we reconstructed the missing phase information by the ptychographic technique. In other words, we visualized the evolution of phase and amplitude information during the generation of electron vortex beam by topological defects of materials. We demonstrated how atomistic topological defect can convert an electron plane wave into an electron vortex beam, from which the amplitude and phase information can be simultaneously resolved by coherent electron nano-diffraction and electron ptychography. 88

The passage of a vortex electron over an inclined grating

“…In the Conclusion, we discuss our final experimental proposal for the detection of the quadrupole (non-paraxial) contribution to the Smith-Purcell radiation. Our method is compatible both with moderate OAM values of ∼ 10 (see also [22][23][24]) and large aspect ratio of Gaussian wave packets.…”

Smith-Purcell radiation of a vortex electron

“…For the currently achieved OAM values of ∼ 1000 [19] (see also [20][21][22]), contributions from both the magnetic moment and the electric quadrupole moment can be, in principle, detected as discussed in the Conclusion.…”