Is the Angular Momentum of an Electron Conserved in a Uniform Magnetic Field?

Greenshields, Colin; Stamps, R. L.; Franke‐Arnold, Sonja; Barnett, Stephen M.

doi:10.1103/physrevlett.113.240404

Cited by 57 publications

(52 citation statements)

References 26 publications

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“…The Landau configuration involves a constant magnetic field in a fixed direction (Bliokh and Nori, 2012a;Gallatin and McMorran, 2012;Greenshields et al, 2012;Landau and Lifshitz, 1977), whilst the AharanovBohm configuration can involve a single line of flux (Bliokh and Nori, 2012a). The vortex propagation direction may be transverse (Gallatin and McMorran, 2012), parallel (Bliokh et al, 2012;Greenshields et al, 2012) to the direction of the field or in an arbitrary orientation (Greenshields et al, 2014), and the interaction between the magnetic moment with the external field leads to interesting dynamics, as we now explain.…”

Section: Dynamics Of the Electron Vortex In External Fieldmentioning

confidence: 99%

“…Solutions of the Schrödinger equation in the presence of several di↵erent field configurations have been investigated (Bliokh et al, 2012;Gallatin and McMorran, 2012;Greenshields et al, 2012Greenshields et al, , 2014Schattschneider et al, 2017;Velasco-Martínez et al, 2016). The Landau configuration involves a constant magnetic field in a fixed direction (Bliokh and Nori, 2012a;Gallatin and McMorran, 2012;Greenshields et al, 2012;Landau and Lifshitz, 1977), whilst the AharanovBohm configuration can involve a single line of flux (Bliokh and Nori, 2012a).…”

Section: Dynamics Of the Electron Vortex In External Fieldmentioning

confidence: 99%

“…Greenshields et al (2014) explored the conceptual issue of conservation of orbital angular momentum for an electron beam in a uniform colinear magnetic field. They showed that the electric field associated with an electron beam with an extended probability distribution, such as that discussed by Lloyd et al (2012b) for electron Bessel beam, when coupled to the external magnetic field, contribute an angular momentum which precisely ensures the conservation of the canonical orbital angular momentum of the electron beam in a magnetic field.…”

Section: A Parallel Propagationmentioning

confidence: 99%

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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: Dynamics Of the Electron Vortex In External Fieldmentioning

confidence: 99%

Section: Dynamics Of the Electron Vortex In External Fieldmentioning

confidence: 99%

Section: A Parallel Propagationmentioning

confidence: 99%

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Electron vortices: Beams with orbital angular momentum

et al. 2017

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“…The orbital magnetic moment of the electron vortex state interacts in unique ways with an external magnetic field, for example, inducing rotations in superpositions of OAM in a longitudinal field [32,33,71], and OAM precession in a transverse field [31]. The kinetic angular momentum of the beam can also vary as the electron vortex beam propagates in a uniform longitudinal magnetic field, although canonical angular momentum remains constant [34,72]. Electron spin angular momentum (SAM) can couple to OAM in non-uniform magnetic and electric fields [73], which may open a new path to producing spin-polarized electrons [74].…”

Section: (B) Free Electron Vortices In a Magnetic Fieldmentioning

confidence: 99%

Origins and demonstrations of electrons with orbital angular momentum

McMorran

Agrawal

Ercius

et al. 2017

Phil. Trans. R. Soc. A.

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“…The same nonrelativistic wave packets were the subject of theoretical analysis in Refs. [10][11][12][13]. In principle, these solutions can be extended to the relativistic domain.…”

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confidence: 99%

A New Twist on Relativistic Electron Vortices

Larocque

Karimi

2017

Physics

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There are important differences between the nonrelativistic and relativistic description of electron beams. In the relativistic case the orbital angular momentum quantum number cannot be used to specify the wave functions and the structure of vortex lines in these two descriptions is completely different. We introduce analytic solutions of the Dirac equation in the form of exponential wave packets and we argue that they properly describe relativistic electron beams carrying angular momentum. DOI: 10.1103/PhysRevLett.118.114801 Introduction.-Recent advances in experiments with relativistic (100-300 keV) electron beams [1-9] carrying orbital angular momentum call for a mathematical description based on the Dirac equation. The generally used Schrödinger equation gives an inadequate description because the differences between the nonrelativistic and relativistic wave functions are essential. It is not only the problem of relativistic corrections, which for 300 keV electrons may amount to about 60%. A more important difference is in the use of the orbital angular momentum quantum number l in the description of electronic states. In the nonrelativistic case both the orbital angular momentum and the total angular momentum are separately conserved while in the relativistic case only the total angular momentum has this property. This has already been pointed out by Dirac who in his first paper on the theory of the electron wrote "This makes a difference between the present theory and the previous spinning electron theory, in which m 2 is constant." Directly related to the problem of orbital angular momentum is a different structure of vortex lines in the two cases.The nonrelativistic wave function in free space is simply a product of the coordinate part and the spin part; the orbital angular momentum and the spin are separately conserved. In the relativistic theory, even in free space, the spin is coupled to the orbital angular momentum and only the total angular momentum is conserved. As a consequence, there are no acceptable solutions of the Dirac equation that are eigenstates of the orbital angular momentum.The proof of this assertion starts with the Dirac equation iℏ∂ t Ψ ¼ HΨ and we assume that L z Ψ ¼ ℏlΨ. By multiplying both sides of the Dirac equation first by ℏl, then by L z , and subtracting the two equations one obtains ½L z ; HΨ ¼ 0. Obviously, also ½L z ; H 2 Ψ ¼ 0. Hence, ðp

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Is the Angular Momentum of an Electron Conserved in a Uniform Magnetic Field?

Cited by 57 publications

References 26 publications

Electron vortices: Beams with orbital angular momentum

Electron vortices: Beams with orbital angular momentum

Origins and demonstrations of electrons with orbital angular momentum

A New Twist on Relativistic Electron Vortices

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