Semiclassical Dynamics of Electron Wave Packet States with Phase Vortices

We consider semiclassical higher-order wave packet solutions of the Schrödinger equation with phase vortices. The vortex line is aligned with the propagation direction, and the wave packet carries a well-defined orbital angular momentum (OAM) $\hslash l$ ($l$ is the vortex strength) along its main linear momentum. The probability current coils around the momentum in such OAM states of electrons. In an electric field, these states evolve like massless particles with spin $l$. The magnetic-monopole Berry curvature appears in momentum space, which results in a spin-orbit-type interaction and a Berry/Magnus transverse force acting on the wave packet. This brings about the OAM Hall effect. In a magnetic field, there is a Zeeman interaction, which, can lead to more complicated dynamics.

Figure 1

Transverse distribution of the probability density $\rho$ in LG beams with $\mathsf{m}=0$ and different values of OAM, $l$. Shown are the directions of common $z$ component and different $\phi$ components of the probability current $\mathbf{j}$.

Figure 2

Central trajectories, Eqs. (5), of the electron states with different values of OAM, $l$, moving in a uniform electric field $\mathbf{E}=E{\mathbf{e}}_y$ (${\mathbf{p}}_0=p_0{\mathbf{e}}_z$, ${\mathbf{r}}_0=\mathbf{0}$, and $l=0$ line corresponds to the classical trajectory).