Abstract
The engineering of the energy dispersion of polaritons in microcavities through nanofabrication or through the exploitation of intrinsic material and cavity anisotropies has demonstrated many intriguing effects related to topology and emergent gauge fields such as the anomalous quantum Hall and Rashba effects. Here we show how we can obtain different Berry curvature distributions of polariton bands in a strongly coupled organic–inorganic two-dimensional perovskite single-crystal microcavity. The spatial anisotropy of the perovskite crystal combined with photonic spin–orbit coupling produce two Hamilton diabolical points in the dispersion. An external magnetic field breaks time-reversal symmetry owing to the exciton Zeeman splitting and lifts the degeneracy of the diabolical points. As a result, the bands possess non-zero integral Berry curvatures, which we directly measure by state tomography. In addition to the determination of the different Berry curvatures of the multimode microcavity dispersions, we can also modify the Berry curvature distribution, the so-called band geometry, within each band by tuning external parameters, such as temperature, magnetic field and sample thickness.
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Data availability
The datasets generated and analysed during the current study are available in the Open Science Framework (OSF) repository via the following link: https://osf.io/x5h7v/?view_only=6a9fa8e1568343f797ec5a76d4626fe1
Change history
12 November 2021
A Correction to this paper has been published: https://doi.org/10.1038/s41565-021-01046-4
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Acknowledgements
We acknowledge P. Cazzato for technical support, I. Tarantini for metal evaporation, and D. Gerace and A. Gianfrate for useful discussions. We acknowledge the project PRIN Interacting Photons in Polariton Circuits (INPhoPOL) (Ministry of University and Scientific Research (MIUR), 2017P9FJBS_001), the project TECNOMED—Tecnopolo di Nanotecnologia e Fotonica per la Medicina di Precisione (Ministry of University and Scientific Research (MIUR) Decreto Direttoriale number 3449 of 4 December 2017, CUP B83B17000010001) and the Accordo bilaterale CNR/RFBR (Russia)—triennio 2021–2023. G.G. gratefully acknowledges the project PERSEO-PERrovskite-based Solar cells: Towards High Efficiency and Long-term Stability (Bando PRIN 2015, Italian Ministry of University and Scientific Research (MIUR) Decreto Direttoriale number 2488 of 4 November 2015, project number 20155LECAJ). D.D.S. and G.M. acknowledge the support of the projects EU QUANTOPOL (846353), Quantum Fluids of Light (ANR-16-CE30-0021), ANR Labex GaNEXT (ANR-11-LABX-0014) and ANR programme ‘Investissements d’Avenir’ through the IDEX-ISITE initiative 16-IDEX-0001 (CAP 20-25). Q.X. gratefully acknowledges the National Natural Science Foundation of China (number 12020101003), strong support from the State Key Laboratory of Low-Dimensional Quantum Physics and a start-up grant from Tsinghua University. The funders had no role in study design, data collection and analysis, decision to publish or preparation of the manuscript. For theoretical information, contact D.D.S. (dmitry.solnyshkov@uca.fr); for materials information, contact L.D.M. (luisa.demarco@nanotec.cnr.it).
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L.P. realized the experiments with the help of M.D.G. and G.L. D.S., G.L. and M.D.G. supervised the experimental part with the help of V.A., F.T. and D.B. L.P, L.D.M., A.C., M.P., C.T.P., Q.X., A.F. and V.M. fabricated the samples. A.M. and C.G. carried out the structure characterization by single-crystal X-ray diffraction and V.O. performed X-ray measurements. D.D.S., G.M., G.L. and L.D. performed the treatment of the experimental data. D.D.S. and G.M. performed analytical calculations. L.P., M.D.G., L.D. with the help of G.L. and D.S. wrote the manuscript with input from all the authors. All authors have contributed to the discussion of the work.
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Extended data
Extended Data Fig. 1 Temperature dependence.
Comparison of the energy vs the ky in-plane momentum dispersion maps of the photoluminescence intensity at 9 T as function of the temperature of a 3 μm-thick single crystal. As the temperature increases, the exciton moves towards higher energy, inducing the increase of the photonic fractions for all polariton bands. d), e), f) Experimental Berry curvature extracted from the polarization-resolved measurements, for the band 2 at D) 4 K, e) 50 K and D) 100 K. The photonic fraction of the band 1 increases from 0.344 at 4 K to 0.366 at 100 K. g) Asymmetry ratio (ratio between B0 and the maximal Bz value on the axis ky = 0 μm−1) versus temperature. The error bars indicate the measurement uncertainty.
Extended Data Fig. 2 Optical Setup.
Sketch of the optical setup.
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Supplementary Information
Supplementary discussion Sections I–X, Figs. 1–9 and Tables 1–4.
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Polimeno, L., Lerario, G., De Giorgi, M. et al. Tuning of the Berry curvature in 2D perovskite polaritons. Nat. Nanotechnol. 16, 1349–1354 (2021). https://doi.org/10.1038/s41565-021-00977-2
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DOI: https://doi.org/10.1038/s41565-021-00977-2
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