Realization of Wilson fermions in topolectrical circuits

Abstract: Wilson fermion (WF) is a fundamental particle in the theory of quantum chromodynamics, originally proposed by Kenneth Wilson to solve the fermion doubling problem, i.e., more fermions than expected when one puts fermionic fields on a lattice. In this Letter, we report a direct observation of the WF in circuit systems. It is found that WFs manifest as topological spin textures analogous to the half skyrmion, half-skyrmion pair, and N\'{e}el skyrmion structures, depending on their mass. Transformations of different WF states are realized by merely tuning the electric elements. Theoretical calculations have shown that the WF with a half-skyrmion profile represents a novel quantum anomalous semimetal phase supporting a chiral edge current [B. Fu et al. npj Quantum Mater. 7, 94 (2022)], but the experimental evidence is still lacking. We experimentally observe the propagation of chiral edge current along the domain-wall separating two circuits with contrast fractional Chern numbers. Our work presents the first experimental evidence for WFs in topolectrical circuits. The nontrivial analogy between the WF state and the skyrmionic structure builds an intimate connection between the two burgeoning fields.