Tuning the Berry curvature in 2D Perovskite

Topological physics and in particular its connection with artificial gauge fields is a forefront topic in different physical systems, ranging from cold atoms to photonics and more recently semiconductor dressed exciton-photon states, called polaritons. Engineering the energy dispersion of polaritons in microcavities through nanofabrication or exploiting the intrinsic material and cavity anisotropies has demonstrated many intriguing effects related to topology and emergent gauge fields. Here, we show that we can control the Berry curvature distribution of polariton bands in a strongly coupled organic-inorganic 2D perovskite single crystal. The spatial anisotropy of the perovskite crystal combined with photonic spin-orbit coupling make emerge two Hamilton's diabolical points in the dispersion. The application of an external magnetic field breaks time reversal symmetry thanks to the exciton Zeeman splitting. It splits the diabolical points degeneracy. The resulting bands show non-zero integral Berry curvature which we directly measure by state tomography. Crucially, we show that we can control the Berry curvature distribution in the band, the so-called band geometry, within the same microcavity.