Turning graphene into an anyonic Chern insulator via surface electromagnon vacuum fluctuations

Sub-wavelength cavities have emerged as a promising platform to realize strong light-matter coupling in condensed matter systems. However, a limiting factor is that the modes of dielectric sub-wavelength cavities have negligible magnetic fields and preserve time-reversal symmetry. In this work, we demonstrate that a cavity formed by confining electromagnons to the interface between vacuum and a magneto-electric material carries a strong magnetic field and breaks time-reversal symmetry. We further show that the quantum fluctuations of these surface electromagnons qualitatively alter the ground state of a nearby graphene layer, inducing a Chern insulating state with a topological gap decaying polynomially with the graphene-substrate distance. The magnetoelectric coupling gives rise to an effective flux attachment, resulting in the quasi-particles tuning into abelian anyons. Our work opens a path to controllably break time-reversal symmetry and induce exotic states through cavity vacuum fluctuations.