Emergent Haldane model and photon-valley locking in chiral cavities

Chirality, often connected with topology, plays a relevant role in both electronic and photonic systems. In this theoretical study, we demonstrate the potential use of quantum fluctuations in a chiral cavity to realize the electronic Haldane model—a model recognized for its pioneering nature yet posing challenges to be realized in materials. Through the recently developed asymptotically-decoupled framework, we derive the emergence of a staggered-flux gauge field resulting from strong light-matter coupling. We show that valley polarization can be achieved by breaking the inversion symmetry of cavity graphene under equilibrium conditions. Reciprocally, the topological properties of graphene could lead to distinct photon-valley locking, linked to the Berry curvatures at opposite valleys. Furthermore, we propose a way to characterize topological phase transitions by probing photons during interband transitions. Our findings highlight the potential of using cavity quantum fluctuations to engineer electronic and photonic properties specific to valleys and topologies, particularly within the realm of strong light-matter coupling. Quantum materials can be engineered using the electromagnetic vacuum fluctuations in a cavity, in a controlled way. The authors show that enhanced quantum fluctuations in a vacuum micro-chiral-cavity can enable the realization of the Haldane model in condensed matter systems, overcoming the challenge of inserting opposite magnetic flux within a solid-state unit cell as required by the model.