One-Way Edge Modes Induced by Synthetic Magnetic Field in Time-Varying LC Circuit

Abstract

A scheme for creating a synthetic magnetic field in an electrical circuit is proposed. The circuit consists of LC resonators arranged in a two-dimensional square lattice and coupled to each other through sinusoidal time-varying capacitors. Under certain assumptions, the dynamical equation of the circuit could be casted into the form of a Schrodinger equation with an effective Hamiltonian. By choosing appropriate values for the elements of the Hamiltonian in analogy with the Hamiltonian of a charged particle under a magnetic field, a synthetic magnetic field appears in the circuit. The robust one-way propagating edge state which is a property of a two dimensional lattice under a magnetic field, was observed in simulations.