Engineering Higher-Order Dirac and Weyl Semimetallic phase in 3D Topolectrical Circuits

We propose a 3D topolectrical (TE) 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 non-reciprocal resistive coupling in the x-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.