Electron vortex beams in a magnetic field and spin filter

Chowdhury, Debanjan; Basu, B.; Bandyopadhyay, P.

doi:10.1103/physreva.91.033812

Cited by 16 publications

(14 citation statements)

References 27 publications

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“…In the non-paraxial and relativistic limits of the Dirac equation, the spin of the electron also plays a role, and the particular distribution is modified by a spinorbit interaction intrinsic to the beam (see section II.D). Note that there is an interesting alternative approach describing electron vortices as a natural consequence of the skyrmion model of a fermion (Bandyopadhyay et al, 2014(Bandyopadhyay et al, , 2016(Bandyopadhyay et al, , 2017Chowdhury et al, 2015), but this will not be discussed any further in this review.…”

Section: Quantum Mechanics Of Electron Vortex Beamsmentioning

confidence: 99%

Electron vortices: Beams with orbital angular momentum

et al. 2017

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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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Section: Quantum Mechanics Of Electron Vortex Beamsmentioning

confidence: 99%

Electron vortices: Beams with orbital angular momentum

et al. 2017

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“…In precedent theoretical investigations (see Refs. [14,15,17,18,21,[25][26][27][28] and references therein), the quantum-mechanical approach was used.…”

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confidence: 99%

Manipulating Twisted Electron Beams

2017

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A theoretical description of twisted (vortex) electrons interacting with electric and magnetic fields is presented, based on Lorentz transformations. The general dynamical equations of motion of a twisted electron with an intrinsic orbital angular momentum in an external field are derived. Methods for the extraction of an electron vortex beam with a given orbital polarization and for the manipulation of such a beam are developed.The discovery of twisted (vortex) electron beams carrying intrinsic orbital angular momentum (OAM) [1] has proven the existence of vortex states of a free electron. Unlike corresponding light vortex beams (which have been successfully used for 25 years [2]), electron beams are charged. Therefore, they also possess significant orbital magnetic moments. Amazingly, a vortex electron in vacuum can be described by the usual Dirac equation for a free particle.In the present work, the system of units = 1, c = 1 is used. We include and c explicitly when this inclusion clarifies the problem. We use the weak-field approximation and neglect terms quadratic in external fields.We give a detailed classical description of dynamics of a twisted particle in external electromagnetic fields. There exists the perfect agreement between relativistic equations of motion for the momentum and the spin in classical electrodynamics and quantum mechanics of spin-1/2 particles in electromagnetic fields (see and references therein). The wonderful agreement with the corresponding classical equations takes place for relativistic spin-1/2 particles in gravity [10]. Relativistic equations of motion for spin-0 [11] and spin-1 [12] particles also fully agree with the corresponding classical equations. This means that the use of an appropriate classical approach for obtaining equations of motion is perfectly admissible.From the viewpoint of quantum mechanics, a twisted electron is a single pointlike particle. Its wave function mirrors a density of a probability to find the electron in a given point of the space. The standard classical model of electron in an atom developed by founders of quantum mechanics is an electron cloud [13] characterizing a spatial distribution of an electron charge. When the atomic electron has a nonzero OAM, the model of the rotating charged cloud is used. We adopt this model to the considered problem. A rotation of the charged electron cloud is a classical counterpart of a current operator describing a motion of the electron about the direction of the intrinsic OAM. In this simple classical picture, an intrinsic OAM originating from the cloud rotation can be parallel to the momentum direction and can be nonzero for a particle at rest. So, the classical description should use some intrinsic rotation which is not associated with the electron momentum p. Besides the intrinsic rotation, an extrinsic rotation of the electron can take place (for example, in an external magnetic field). The latter rotation depends on the electron momentum and is defined by the extrinsic OAM r × p. Quantum mechanics uses...

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“…For non-paraxial beams with tilted vortices Bessel beams correspond to the situation when the polar angle θ 0 takes an arbitrary non-zero value. Within this framework, we have investigated the propagation of electron vortex beams in a magnetic field [11] and have also theoretically studied the orbital angular momentum (OAM) Hall effect and spin Hall effect of EVBs interacting with a laser field [12]. Our motivation here is to propose a unified framework towards the dynamics of OVBs and EVBs from the perspective of the geometric phase.…”

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confidence: 99%

“…This gives rise to spin Hall effect. v a in eqn (11) can be rewritten in terms of the unit vector u = p p and its time derivative ˙ u as…”

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confidence: 99%

“…The stability can be attained if the effect of the Gouy phase associated with the superposition of Laguerre-Gaussian modes generating OVBs can be regulated [22]. A similar situation may be developed for the propagation of EVBs in an external magnetic field [11]. The vortex structure of light emerging from a fractional phase step is characterised by a chain of alternating vortices such that every pair of it forms a hairpin when the vortices converge at a common turning point [23,24].…”

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Unified Approach towards the Dynamics of Optical and Electron Vortex Beams

2016

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We have proposed a unified framework towards the dynamics of optical and electron vortex beams from the perspective of the geometric phase and the associated Hall effects. The unification is attributed to the notion that the spin degrees of freedom of a relativistic particle, either massive or massless, are associated with a vortex line. Based on a cylindrical coordinate formulation, which leads to a local vortex structure related to orbital angular momentum (OAM), it can be shown that, when electron vortex beams (EVBs) move in an external electric field, paraxial beams give rise to an OAM Hall effect, and nonparaxial beams with tilted vortices initiate a spin Hall effect in free space as well as in an external field. A similar analysis reveals that the paraxial optical vortex beams (OVBs) in an inhomogeneous medium induce an OAM Hall effect, whereas nonparaxial beams with tilted vortices drive the spin Hall effect. Moreover, both OVBs and EVBs with tilted vortices give rise to OAM states with an arbitrary fractional value.

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Electron vortex beams in a magnetic field and spin filter

Cited by 16 publications

References 27 publications

Electron vortices: Beams with orbital angular momentum

Electron vortices: Beams with orbital angular momentum

Manipulating Twisted Electron Beams

Unified Approach towards the Dynamics of Optical and Electron Vortex Beams

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