Quantum Hall phase and chiral edge states simulated by a coupled dipole method

Abstract

We present theoretical modeling of the quantum Hall phase and chiral edge states in a gyroelectric photonic crystal. The theoretical framework represented here is based on a coupled dipole method, which is a direct counterpart of the tight-binding approximation. We confirm that gyrotropic coupling produces a band gap characterized by a nonzero Chern number. Gapless edge states appear at an interface between a gyroeletric photonic crystal and a vacuum. At a domain wall between media of positive and negative gyrotropy, topological edge states that are analogous to the Jackiw-Rebbi states are observed. Propagation of the chiral edge states is also simulated in real space under excitation of an external dipole source. This analysis provides a toy model to describe the quantum Hall phase in a purely optical manner, without using a mapping or an analogy of the electron wave function in the quantum Hall effect.