Topological states in electric circuit

Abstract

Based on the correspondence between tight-binding Hamiltonian in condensed matter physics and the Kirchhoff’s current equations in lumped parameters circuits, profuse topological states can be mapped from the former to the latter. In this article, the electric-circuit realizations of 1D SSH model, 3D nodal-line and Weyl semimetals are devised and elaborated, in which the edge states, surface drum-head and Fermi-arc states are appearing on the surface of the circuit lattice. Of these circuits, the effective hopping terms in Hamiltonian have high degree of freedom. The hopping strength, distance and dimension are easy to tune, and therefore our design is convenient to be extended to non-Hermitian and four or higher dimensional cases, making the fancy states that hard to reach in conventional condensed matter now at our fingertips. Besides, the electric circuit has the advantage of plentiful functional elements and mature manufacture techniques, thus being a promising platform to explore exotic states of matter.