Berry phase and anomalous velocity of Weyl fermions and Maxwell photons

Abstract

We consider two systems of wave equations whose wave-packet solutions have trajectories that are altered by the "anomalous velocity" effect of a Berry curvature. The first is the matrix Weyl equation describing cyclotron motion of a charged massless fermion. The second is Maxwell equations for the whispering-gallery modes of light in a cylindrical waveguide. In the case of the massless fermion, the anomalous velocity is obscured by the contribution from the magnetic moment. In the whispering gallery modes the anomalous velocity causes the circumferential light ray to creep up the cylinder at the rate of one wavelength per orbit, and can be identified as a continuous version of the Imbert-Federov effect.