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

## TL;DR

This paper theoretically demonstrates how photonic analogs of transition metal dichalcogenides can exhibit quantum valley Hall effects and perfect valley filtering, controlled by photonic spin-orbit coupling and Zeeman fields.

## Contribution

It introduces a simple photonic lattice model to realize quantum valley Hall and anomalous Hall effects, enabling control over valley-polarized modes and perfect valley filtering.

## Key findings

- Valley-polarized propagating modes exist at interfaces between TMD analogs.
- Photonic spin-orbit coupling controls the number and direction of interface modes.
- The system acts as a perfect valley filter under certain conditions.

## Abstract

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.