# Photonic Versus Electronic Quantum Anomalous Hall Effect

## TL;DR

This paper compares photonic and electronic quantum anomalous Hall effects in honeycomb lattices, highlighting differences in topological phases, and introduces an all-optical method to control topological transitions in photonic systems.

## Contribution

It derives the topological phase diagram for both photon and electron systems, revealing key differences due to spin-orbit coupling and demonstrating optical control of topological phases in photonics.

## Key findings

- Photonic systems exhibit a topological transition absent in electronic systems.
- The winding number of SOC differs: 2 for photons, 1 for electrons.
- All-optical control of topological phase transitions is possible via exciton-polaritons.

## Abstract

We derive the diagram of the topological phases accessible within a generic Hamiltonian describing quantum anomalous Hall effect for photons and electrons in honeycomb lattices in presence of a Zeeman field and Spin-Orbit Coupling (SOC). The two cases differ crucially by the winding number of their SOC, which is 1 for the Rashba SOC of electrons, and 2 for the photon SOC induced by the energy splitting between the TE and TM modes. As a consequence, the two models exhibit opposite Chern numbers $\pm 2$ at low field. Moreover, the photonic system shows a topological transition absent in the electronic case. If the photonic states are mixed with excitonic resonances to form interacting exciton-polaritons, the effective Zeeman field can be induced and controlled by a circularly polarized pump. This new feature allows an all-optical control of the topological phase transitions.