Electric circuit simulation of Floquet topological insulators in Fourier space

Abstract

We present a method for simulating any non-interacting and time-periodic tight-binding Hamiltonian in Fourier space using electric circuits made of inductors and capacitors. We first map the time-periodic Hamiltonian to a Floquet Hamiltonian, which converts the time dimension into a Floquet dimension. In electric circuits, this Floquet dimension is simulated as an extraspatial dimension without any time dependency in the electrical elements. The number of replicas needed in the Floquet Hamiltonian depends on the frequency and strength of the drive. We also demonstrate that we can detect the topological edge states (including the anomalous edge states in the dynamical gap) in an electric circuit by measuring the two-point impedance between the nodes. Our method paves a simple and promising way to explore and control Floquet topological phases in electric circuits.