Observation of Anti-helical edge states in Topolectrical Circuit

Chiral edge modes (CEMs), the defining feature of the quantum Hall effect, propagate unidirectionally along opposite edges of a ribbon geometry. Recent theoretical studies have revealed the existence of unconventional anti-Chiral edge modes(aCEMs) that copropagate along parallel edges. Extending this concept, anti-helical edge modes (aHEMs) can be viewed as a time-reversal-related pair of aCEMs, analogous to the helical edge modes (HEMs) in the quantum spin Hall effect. Here, we realize and observe aHEMs in a Topolectrical (TE) circuit engineered to mimic a monolayer system with effective real, imaginary as well as non-reciprocal couplings realized with capacitors, resistors and Op-Amps respectively. The circuit Laplacian reproduces the effective Hamiltonian governing the desired topological phase. Through impedance spectroscopy and reconstruction of the admittance band structure, we identify clear evidence of aHEMs, including pseudospin-selective excitations and energy-shifted Dirac points in the bulk spectrum. These results establish electrical circuit networks as a versatile and tunable platform for exploring nontrivial topological phenomena and may inspire future designs of reconfigurable devices with robust edge transport.