Link between the photonic and electronic topological phases in artificial graphene

In recent years the study of topological phases of matter has emerged as a very exciting field of research, both in photonics and in electronics. However, up to now the electronic and photonic properties have been regarded as totally independent. Here we establish a link between the electronic and the photonic topological phases of the same material system and theoretically demonstrate that they are intimately related. We propose a realization of the Haldane model as a patterned two-dimensional electron gas and determine its optical response using the Kubo formula. It is shown that the electronic and photonic phase diagrams of the patterned electron gas are strictly related. In particular, the system has a trivial photonic topology when the inversion symmetry is the prevalent broken symmetry, whereas it has a nontrivial photonic topology for a dominant broken time-reversal symmetry, similar to the electronic case. To confirm these predictions, we numerically demonstrate the emergence of topologically protected unidirectional electromagnetic edge states at the interface with a trivial photonic material.