Topology of Wilson-loop spectrum and periodic evolution of surface-state Fermi arc

Abstract: Wilson-loop has been widely used to characterize the topological property of topological insulators, high order topological insulators and topological semimetals. Both bulk topological invariants and nontrivial boundary properties can be deduced from the topology of Wilson-loop spectrum. However, no attempt has been made to observe it. In this letter we demonstrate the topology of Wilson-loop spectrum can be observed by using the existing technology for observing surface-state Fermi arc. We predict that the surface-state Fermi arc sweeps the whole surface Brillouin zone in a continuous periodic process and thus generates a surface that is topologically equivalent to the Wilson-loop spectrum. So by observing the evolution of surface-state Fermi arc in the periodic process we can get the topology of Wilson-loop spectrum.