When an electron beam is incident from a Weyl semimetal (WSM) onto another material and undergoes reflection, it exhibits a spatial shift. This shift depends on the in-plane wave vectors and displays vortex structures in the incident pocket (the projection of the Fermi surface) or on the pocket edge. According to Yang and He [Phys. Rev. B 110, 195302 (2024)], based on the quantization of Berry flux on the Fermi surface of a type-I WSM, the total vortex number corresponds to the topological charge carried by the Weyl point, while the number of edge vortices equals that of the Fermi arcs connected to the incident pocket. However, when the incident material is a type-II WSM, the Fermi surface of incidence is a hyperboloid (the Fermi pocket is a two-sheeted hyperbola), which is fragmental and nonenclosed. In this case, the quantization condition breaks down and the definition of interface topology requires revision. We introduce a composite loop for the incident sheet comprising two segments: one tracing the sheet edge and the other winding back across the hyperbola in the remote. It is found that the accumulation of reflection shift along the composite loop serves to characterize the interface topology. The edge segment yields both the number of edge vortices and that of Fermi arcs connected to the incident sheet, whereas the crossing segment counts the lost vortices—those absent in the open Fermi surface but expected in a closed one. A vortex loss in one sheet mandates the emergence of an antivortex in the other. Our findings enrich the understanding about topological properties of materials with open Fermi surfaces.

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• Geometric & topological phases
• Surface states
• Solid-solid interfaces
• Weyl semimetal
• Transfer matrix method
• k dot p method