The geometric phase and the geometrodynamics of relativistic electron vortex beams

Abstract

We have studied here the geometrodynamics of relativistic electron vortex beams from the perspective of the geometric phase associated with the scalar electron encircling the vortex line. It is pointed out that the electron vortex beam carrying orbital angular momentum is a natural consequence of the skyrmion model of a fermion. This follows from the quantization procedure of a fermion in the framework of Nelson's stochastic mechanics when a direction vector (vortex line) is introduced to depict the spin degrees of freedom. In this formalism a fermion is depicted as a scalar particle encircling a vortex line. It is here shown that when the Berry phase acquired by the scalar electron encircling the vortex line involves quantized Dirac monopole we have paraxial (non-paraxial) beam when the vortex line is parallel (orthogonal) to the wavefront propagation direction. Non-paraxial beams incorporate spin-orbit interaction. When the vortex line is tilted with respect to the propagation direction the Berry phase involves non-quantized monopole. The temporal variation of the direction of the tilted vortices is studied here taking into account the renormalization group flow of the monopole charge and it is predicted that this gives rise to spin Hall effect.

Accepted for publication in Proceedings of Royal Society A

References in corpus (7)

• Semiclassical Dynamics of Electron Wave Packet States with Phase Vortices
• Spatio-temporal vortex beams and angular momentum
• Geometrodynamics of polarized light: Berry phase and spin Hall effect in a gradient-index medium
• Current-induced domain wall motion in Rashba spin-orbit system
• Topological spin transport of relativistic electron
• Spin Hall utilizing U(1) and SU(2) gauge fields
• Inertial effect on spin orbit coupling and spin transport

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