Spin effects in electron vortex states

Boxem, Ruben Van; Verbeeck, Johan; Partoens, B.

doi:10.1209/0295-5075/102/40010

Cited by 17 publications

(15 citation statements)

References 34 publications

(54 reference statements)

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“…Even the most noticeable effect of non-zero probability density in the center of a vortex mode with s = − /2, Fig. 15(a), in practice becomes non-observable [179] due to decoherence effects related to the source-size broadening, which blurs the vortex core even in the non-relativistic scalar case [180] This reflects the well known fact that the orbital and spin AM contribute to the magnetic moment with the g = 1 and g = 2 factors, respectively [3]. Note that the magnetic moment (2.60) corresponds to free-space Dirac-Bessel solutions.…”

Section: Spin-orbit Interaction Phenomenamentioning

confidence: 99%

Theory and applications of free-electron vortex states

Bliokh¹,

Иванов²,

Guzzinati³

et al. 2017

Physics Reports

302

347

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Both classical and quantum waves can form vortices: with helical phase fronts and azimuthal current densities. These features determine the intrinsic orbital angular momentum carried by localized vortex states. In the past 25 years, optical vortex beams have become an inherent part of modern optics, with many remarkable achievements and applications. In the past decade, it has been realized and demonstrated that such vortex beams or wavepackets can also appear in free electron waves, in particular, in electron microscopy. Interest in free-electron vortex states quickly spread over different areas of physics: from basic aspects of quantum mechanics, via applications for fine probing of matter (including individual atoms), to high-energy particle collision and radiation processes. Here we provide a comprehensive review of theoretical and experimental studies in this emerging field of research. We describe the main properties of electron vortex states, experimental achievements and possible applications within transmission electron microscopy, as well as the possible role of vortex electrons in relativistic and high-energy processes. We aim to provide a balanced description including a pedagogical introduction, solid theoretical basis, and a wide range of practical details. Special attention is paid to translate theoretical insights into suggestions for future experiments, in electron microscopy and beyond, in any situation where free electrons occur.

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Section: Spin-orbit Interaction Phenomenamentioning

confidence: 99%

Theory and applications of free-electron vortex states

Bliokh¹,

Иванов²,

Guzzinati³

et al. 2017

Physics Reports

302

347

View full text Add to dashboard Cite

show abstract

“…First, electron beams in transmission electron microscopes (TEMs) are unpolarized. Second, these are strongly paraxial and SOI effects become negligible under such conditions [16]. Nevertheless, there is still theoretical interest in relativistic electron vortex states, and two recent works [17,18] revisited vortex solutions and AM properties of the Dirac equation, in slightly different contexts to [9].…”

Section: Introductionmentioning

confidence: 99%

Position, spin, and orbital angular momentum of a relativistic electron

2017

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General rightsThis document is made available in accordance with publisher policies. Please cite only the published version using the reference above. Motivated by recent interest in relativistic electron vortex states, we revisit the spin and orbital angular momentum properties of Dirac electrons. These are uniquely determined by the choice of the position operator for a relativistic electron. We consider two main approaches discussed in the literature: (i) the projection of operators onto the positive-energy subspace, which removes the Zitterbewegung effects and correctly describes spin-orbit interaction effects, and (ii) the use of Newton-Wigner-Foldy-Wouthuysen operators based on the inverse Foldy-Wouthuysen transformation. We argue that the first approach [previously described in application to Dirac vortex beams in K. Y. Bliokh et al., Phys. Rev. Lett. 107, 174802 (2011)] has a more natural physical interpretation, including spin-orbit interactions and a nonsingular zero-mass limit, than the second one [S. M.

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“…For states that do show spin-orbit mixing, the spin polarization across the beam is nonuniform rendering the spin and orbital degrees of freedom inherently inseparable.Introduction-The concept of light beams carrying orbital angular momentum along the propagation axis has been widely utilized in modern optics [1][2][3]. Based on analogies of the governing wave equations, vortex beams have also been predicted and generated for electrons [4][5][6][7][8][9][10][11][12] and neutrons [13], as well as proposed for atoms [14,15]. This promises the ability to probe and manipulate matter on smaller length scales, but also opens up the possibility to consider the interaction of vortex beams with external fields [16][17][18][19][20], other vortex beams [21,22] and atoms [23].In the simplest description these vortex beams are scalar and obey the paraxial Schrödinger equation.…”

mentioning

confidence: 99%

Nonuniform Currents and Spins of Relativistic Electron Vortices in a Magnetic Field

2017

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We present a relativistic description of electron vortex beams in a homogeneous magnetic field. Including spin from the beginning reveals that spin-polarized electron vortex beams have a complicated azimuthal current structure, containing small rings of counterrotating current between rings of stronger corotating current. Contrary to many other problems in relativistic quantum mechanics, there exists a set of vortex beams with exactly zero spin-orbit mixing in the highly relativistic and nonparaxial regime. The well defined phase structure of these beams is analogous to simpler scalar vortex beams, owing to the protection by the Zeeman effect. For states that do show spin-orbit mixing, the spin polarization across the beam is nonuniform rendering the spin and orbital degrees of freedom inherently inseparable.Introduction-The concept of light beams carrying orbital angular momentum along the propagation axis has been widely utilized in modern optics [1][2][3]. Based on analogies of the governing wave equations, vortex beams have also been predicted and generated for electrons [4][5][6][7][8][9][10][11][12] and neutrons [13], as well as proposed for atoms [14,15]. This promises the ability to probe and manipulate matter on smaller length scales, but also opens up the possibility to consider the interaction of vortex beams with external fields [16][17][18][19][20], other vortex beams [21,22] and atoms [23].In the simplest description these vortex beams are scalar and obey the paraxial Schrödinger equation. Going beyond the paraxial approximation reveals a linking between the spin and orbital degrees of freedom arising whenever the beam is tightly confined, complicating the vortex structure [24,25]. And whereas light beams as solutions of Maxwell's equation are naturally relativistic, for particles it is important to distinguish between the nonrelativisitic regime based on Schrödinger's equation and the relativistic regime covered by the Dirac equation.Whether or not a nonrelativistic description suffices depends not only on the energy of the electron beam involved, but also on the importance the spin of the particle in the interaction in question, as spin is naturally included in the Dirac equation [26,27]. For electrons traveling through a magnetic field it is of particular importance to take the spin into account, because it interacts strongly with the field.We analytically solve the Dirac equation for an electron in a homogeneous magnetic field, a problem first considered by Landau [27,28]. The interaction with the magnetic field confines the beam and gives rise to a set of discrete energy levels (Landau levels) [16,28]. On top of that the Zeeman effect shifts the energy of the positive and negative spin states relative to each other. The quantized Landau and Zeeman contributions to the energy determine which states undergo spin-orbit mixing with each other and completely forbid spin-orbit mixing

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Spin effects in electron vortex states

Cited by 17 publications

References 34 publications

Theory and applications of free-electron vortex states

Theory and applications of free-electron vortex states

Position, spin, and orbital angular momentum of a relativistic electron

Nonuniform Currents and Spins of Relativistic Electron Vortices in a Magnetic Field

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