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Topological physics and in particular its connection with artificial gaugefields is a forefront topic in different physical systems, ranging from coldatoms to photonics and more recently semiconductor dressed exciton-photonstates, called polaritons. Engineering the energy dispersion of polaritons inmicrocavities through nanofabrication or exploiting the intrinsic material andcavity anisotropies has demonstrated many intriguing effects related totopology and emergent gauge fields. Here, we show that we can control the Berrycurvature distribution of polariton bands in a strongly coupledorganic-inorganic 2D perovskite single crystal. The spatial anisotropy of theperovskite crystal combined with photonic spin-orbit coupling make emerge twoHamilton's diabolical points in the dispersion. The application of an externalmagnetic field breaks time reversal symmetry thanks to the exciton Zeemansplitting. It splits the diabolical points degeneracy. The resulting bands shownon-zero integral Berry curvature which we directly measure by statetomography. Crucially, we show that we can control the Berry curvaturedistribution in the band, the so-called band geometry, within the samemicrocavity.

Tuning the Berry curvature in 2D Perovskite