The Geometric phase and fractional orbital angular momentum states in electron vortex beams

TL;DR

This paper explores how geometric phase influences fractional orbital angular momentum states in electron vortex beams, revealing their instability during propagation and how external magnetic fields can stabilize these states.

Contribution

It introduces a skyrmionic model perspective to fractional OAM in EVBs, linking geometric phase, spin-orbit interaction, and vortex tilt effects.

Findings

Fractional OAM states are induced by geometric phase and spin-orbit interaction.

RG flow causes fractional OAM states to be unstable during propagation.

External magnetic fields and radial mode choices can stabilize fractional OAM states.

Abstract

We study here fractional orbital angular momentum (OAM) states in electron vortex beams (EVB) from the perspective of geometric phase. We have considered the skyrmionic model of an electron, where it is depicted as a scalar electron orbiting around the vortex line, which gives rise to the spin degrees of freedom. The geometric phase acquired by the scalar electron orbiting around the vortex line induces the spin-orbit interaction, which leads to the fractional OAM states with non-quantized monopole charge associated with the corresponding geometric phase. This involves tilted vortex in EVBs. The monopole charge undergoes the renormalization group (RG) flow, which incorporates a length scale dependence making the fractional OAM states unstable upon propagation. It is pointed out that when EVBs move in an external magnetic field, the Gouy phase associated with the Laguerre-Gaussian modes modifies the geometric phase factor and a proper choice of the radial index helps to have a stable fractional OAM state.