The recent prediction and subsequent creation of electron vortex beams in a number of laboratories occurred after almost 20 years had elapsed since the recognition of the physical significance and potential for applications of the orbital angular momentum carried by optical vortex beams. A rapid growth in interest in electron vortex beams followed, with swift theoretical and experimental developments. Much of the rapid progress can be attributed in part to the clear similarities between electron optics and photonics arising from the functional equivalence between the Helmholtz equations governing the free space propagation of optical beams and the time-independent Schrödinger equation governing freely propagating electron vortex beams. There are, however, key di↵erences in the properties of the two kinds of vortex beams. This review is concerned primarily with the electron type, with specific emphasis on the distinguishing vortex features: notably the spin, electric charge, current and magnetic moment, the spatial distribution as well as the associated electric and magnetic fields. The physical consequences and potential applications of such properties are pointed out and analysed, including nanoparticle manipulation and the mechanisms of orbital angular momentum transfer in the electron vortex interaction with matter.

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Following the very recent experimental realization of electron vortices, we consider their interaction with matter, in particular, the transfer of orbital angular momentum in the context of electron energy-loss spectroscopy, and the recently observed dichroism in thin film magnetized iron samples. We show here that orbital angular momentum exchange does indeed occur between electron vortices and the internal electronic-type motion, as well as center-of-mass motion of atoms in the electric dipole approximation. This contrasts with the case of optical vortices where such transfer only occurs in transitions involving multipoles higher than the dipole. The physical basis of the observed dichroism is explained.

Electron vortices are shown to possess electric and magnetic fields by virtue of their quantized orbital angular momentum and their charge and current density sources. The spatial distributions of these fields are determined for a Bessel electron vortex. It is shown how these fields lead naturally to interactions involving coupling to the spin magnetic moment and spin-orbit interactions which are absent for ordinary electron beams. The orders of magnitude of the effects are estimated here for ȧngström scale electron vortices generated within a typical electron microscope.

Chiral electron vortex beams, carrying well-defined orbital angular momentum (OAM) about the propagation axis, are potentially useful as probes of magnetic and other chiral materials. We present an effective operator, expressible in a multipolar form, describing the inelastic processes in which electron vortex beams interact with atoms, including those present in Bose-Einstein condensates, involving exchange of OAM. We show clearly that the key properties of the processes are dependent on the dynamical state and location of the atoms involved as well as the vortex beam characteristics. Our results can be used to identify scenarios in which chiral-specific electron vortex spectroscopy can probe magnetic sublevel transitions normally studied using circularly polarized photon beams with the advantage of atomic scale spatial resolution.Particle vortices, most notably electron vortices (EVs), are currently the focus of much interest following the prediction by Bliokh et al.[1] and their experimental realization in a number of laboratories, using various techniques [2][3][4][5][6][7]. This area has recently emerged after much fruitful research has been carried out on optical vortices (OVs) over the last two decades or so, which has led to a wealth of fundamental knowledge and significant applications [8][9][10]. Both the optical and electron vortices are characterised by the singular nature of their wavefronts, with a well defined vortex core and quantised orbital angular momentum (OAM) about the vortex axis. The general expectation is that in all cases the vortex OAM should play an important role in the interaction of the vortex with matter. However, in the case of an OV, a dipole active transition involves exchange of OAM with the centre of mass only [11,12], a finding which has been confirmed experimentally [13,14]. The development of OAM-based OV beam spectroscopy has been hampered by the weakness of optical multipolar transitions. In contrast, we have recently demonstrated theoretically that OAM can be transferred efficiently from an EV beam to atomic electrons through dipole active transitions [12,15] and experimentally a dichroic electron energy-loss spectroscopic signal has been detected [3], opening up the prospect of chiral specific electron vortex beam spectroscopy (CEVBS) based on OAM selection rules. Using a new analytical method, we present an effective operator in the context of OAM transitions in quantum systems using electron vortex beams. This is important for the realization of CEVBS as it allows the derivation of the key OAM-and chiral-related characteristics, going beyond the derivation of the dipole OAM selection rules to also include a multipolar expansion and the spatial dependence of the quantum transitions involved. The new results suggest that a confocal spectroscopy set-up could be used to obtain optical activity or X-ray circular dichroic spectroscopy at atomic resolution, for characterization of chiral or magnetic materials and for the determination of the coherent state of a coldatom con...