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

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