Realization of ideal unconventional Weyl states with arbitrary topological charge

Weyl points in crystalline materials can be treated as magnetic monopoles in momentum space, with topological charges inscribed by Chern numbers. The main method of finding Weyl states with topological charges greater than one, i.e., unconventional Weyl states, is to take advantage of crystal symmetries, but the maximum topological charge that can be achieved is four. Here we provide a unified scheme for realizing a pair of Weyl points using long-range spin-orbit coupling. This scheme requires no additional symmetry other than the translational symmetry of the crystal and allows the realization of the Weyl point with arbitrary topological charges. We give a concrete method for its realization in a circuit system and verify it experimentally. This discovery reveals a scheme for realizing ideal unconventional Weyl states and using long-range spin-orbit coupling for exotic states.