Realization of Wilson fermions in topolectrical circuits

Abstract

Abstract The Wilson fermion (WF) is a fundamental particle in the theory of quantum chromodynamics. Theoretical calculations have shown that the WF with a half skyrmion profile represents a quantum anomalous semimetal phase supporting a chiral edge current, but the experimental evidence is still lacking. In this work, we report a direct observation of the WF in circuit systems. We find that WFs manifest as topological spin textures analogous to the half skyrmion, half-skyrmion pair, and Néel skyrmion structures, depending on their mass. Transformations of different WF states are realized by tuning the electric elements. We further experimentally observe the propagation of chiral edge current along the domain-wall separating two circuits with contrast fractional Chern numbers. Our work provides 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.