Anomalous shift in scattering from topological nodal-ring semimetals

An electron beam may experience an anomalous spatial shift during an interface scattering process. Here, we investigate this phenomenon for reflection from mirror-symmetry-protected nodal-ring semimetals, which are characterized by an integer topological charge ${\chi }_h$. We show that the shift is generally enhanced by the presence of nodal rings, and the ring’s geometry can be inferred from the profile of shift vectors in the interface momentum plane. Importantly, the anomalous shift encodes the topological information of the ring, where the circulation of the shift vector field ${\kappa }_s$ over a semicircle is governed by the topological charge, with a simple relationship: ${\kappa }_s=-2\pi {\chi }_h$. Furthermore, we demonstrate that the shift and its circulation reflect distinct features of topological phase transitions of the charged rings. This study uncovers a novel physical signature of topological nodal rings and positions anomalous scattering shifts as a powerful tool for probing topological band structures.