Quantum Valley Hall Effect and Perfect Valley Filter Based on Photonic Analogs of Transitional Metal Dichalcogenides

We consider theoretically staggered honeycomb lattices for photons which can be viewed as photonic analogs of transitional metal dichalcogenides (TMD) monolayers. We propose a simple realization of a photonic Quantum Valley Hall effect (QVHE) at the interface between two TMD analogs with opposite staggering on each side. This results in the formation of valley-polarized propagating modes whose existence relies on the difference between the valley Chern numbers, which is a $\mathbb{Z}_2$ topological invariant. We show that the magnitude of the photonic spin-orbit coupling based on the energy splitting between TE and TM photonic modes allows to control the number and propagation direction of these interface modes. Finally, we consider the interface between a staggered and a regular honeycomb lattice subject to a non-zero Zeeman field, therefore showing Quantum Anomalous Hall Effect (QAHE). In such a case, the topologically protected one-way modes of the QAHE become valley-polarized and the system behaves as a perfect valley filter.