Polariton vortex Chern insulator [Invited]

Abstract

We propose a vortex Chern insulator, motivated by recent experimental demonstrations on programmable arrangements of cavity polariton vortices by [S. Alyatkin et al., arXiv , ArXiv:2207.01850 ( 2022 ) 10.48550/arXiv.2207.01850 ] and [J. Wang et al, Natl. Sci. Rev. 10 , Nwac096 ( 2022 ) 10.1093/nsr/nwac096 ]. In the absence of any external fields, time-reversal symmetry is spontaneously broken through polariton condensation into structured arrangements of localized co-rotating vortices. We characterize the response of the rotating condensate lattice by calculating the spectrum of Bogoliubov elementary excitations and observe the crossing of edge-states, of opposite vorticity, connecting bands with opposite Chern numbers. The emergent topologically nontrivial energy gap stems from inherent vortex anisotropic polariton-polariton interactions and does not require any spin-orbit coupling, external magnetic fields, or elliptically polarized pump fields.