Vortex of beam shift induced by mono-chiral interface states

Abstract

If an electron beam hits onto the interface of a Weyl-node-mismatch junction, a shift of the beam center on the interface happens when the beam is reflected or transmitted, where the junction consists of two materials of the same Weyl semimetal and one of them is rotated with respect to the other by an angle. We calculate the longitudinal and transverse shift components (the Goos–Hänchen and Imbert–Fedorov shifts). The reflection shift for total reflection cases is much more remarkable than the shift for transmitted cases. There exists a semi-vortex structure of the reflection shift on the in-plane k-space. The vortex is induced by the touch between bulk bands and interface bands. The formation of such interface bands is explained by the pulley-group model, in which the Weyl cones serve as wheels and the surface and interface bands act as ropes. A surface rope connects wheels of opposite chiralities, and an interface rope links the wheels for the two side materials of the same chirality.