Chiral surface and hinge states in higher-order Weyl semimetallic circuits

We propose a 3D topolectrical network that can be tuned to realize various higher-order topological gapless and chiral phases. We first study a higher-order Dirac semimetal phase that exhibits a hinge-like Fermi arc linking the Dirac points. This circuit can be extended to host highly tunable first- and second-order Weyl semimetal phases by introducing a nonreciprocal resistive coupling in the $x\text{−}y$ plane that breaks time reversal symmetry. The first- and second-order Weyl points are connected by zero-admittance surface and hinge states, respectively. We also study the emergence of first- and second-order chiral modes induced by resistive couplings between similar nodes in the $z$ direction. These modes, respectively, occur in the midgap of the surface and hinge admittance bands in our circuit model without the need for any external magnetic field.