Abstract
A photonic topological insulator features robust directional propagation and immunity to defect perturbations of the edge/surface state. Exciton-polaritons, that is, the hybrid quasiparticles of excitons and photons in semiconductor microcavities, have been proposed as a tunable nonlinear platform for emulating topological phenomena. However, mainly due to excitonic material limitations, experimental observations so far have not been able to enter the nonlinear condensation regime or only show localized condensation in one dimension. Here we show a topological propagating edge state with polariton condensation at room temperature and without any external magnetic field. We overcome material limitations by using excitonic CsPbCl3 halide perovskites with a valley Hall lattice design. The polariton lattice features a large bandgap of 18.8 meV and exhibits strong nonlinear polariton condensation with clear long-range spatial coherence across the critical pumping density. The geometric parameters and material composition of our nonlinear many-body photonic system platform can in principle be tailored to study topological phenomena of other interquasiparticle interactions.
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Data availability
The main data supporting the findings of this study are available within the paper. Extra data are available from the corresponding authors upon reasonable request. Source data are provided with this paper.
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Acknowledgements
We thank S. Klembt and T. Cao for discussions and A. Gao from SVOTEK Inc. for assisting with the high-quality DBR mirror coating. W.B. thanks the National Science Foundation for CAREER support (award DMR-2414131) and the Rensselaer Polytechnic Institute for start-up support. W.B., K.P. and W.L. acknowledge support from the Office of Naval Research (awards N00014-21-1-2099 and N00014-22-1-2322) and from Nebraska Public Power District through the Nebraska Center for Energy Sciences Research. X.Z. and K.P. thank the Gordon and Betty Moore Foundation (award 5722) and the Ernest S. Kuh Endowed Chair Professorship for support. J.D.H.R. and L.G. acknowledge funding from the National Science Foundation (award PHY-1847240). Work performed at the Center for Nanoscale Materials, a US Department of Energy Office of Science User Facility, was supported by the US DOE, Office of Basic Energy Sciences, under contract DE-AC02-06CH11357. The research was partly performed in the Nebraska Nanoscale Facility: National Nanotechnology Coordinated Infrastructure and the Nebraska Center for Materials and Nanoscience, supported by the National Science Foundation (award ECCS-2025298) and the Nebraska Research Initiative.
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Contributions
W.B. and K.P. conceived and initiated the project. K.P. performed all optical measurements. W.L. fabricated the microcavity samples with assistance from K.P., C.T. and X.H. W.L. and K.P. grew and characterized the perovskite materials. M.S., J.D.H.R. and L.G. performed all the theoretical analysis and calculations with assistance from K.P. K.P. and W.B. analysed all the data. L.G. suggested the initial design. L.Y. provided valuable insight and suggestions. W.B. and X.Z. supervised the whole project. K.P., W.L., M.S. and W.B. prepared the initial draft of the manuscript. All authors participated in revising the manuscript.
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Extended data
Extended Data Fig. 1 The AFM image of the patterned PMMA.
For this sample, the PMMA spacer has a thickness of ~70 nm. The topological interface can be clearly observed.
Extended Data Fig. 2 Room-temperature absorption and PL spectrum of a CsPbCl3 single crystal.
The sample shows a strong and stable excitonic absorption peak at room temperature. The corresponding exciton energy peak was extracted as 3.042 eV.
Extended Data Fig. 3 PL spectra of the CsPbCl3 plate before and after treatments of O2 plasma and MIBK/IPA developments.
a-I-II, The real-space PL images of a single perovskite crystal with non-resonant excitation before and after the treatments of 2 minutes O2 plasma and 30 s soaking in MIBK/IPA and 15 s rinsing in IPA. b, The corresponding PL spectra before and after treatments. Here, after the treatments, the perovskite plate still shows high PL intensity. Scale bars in a: 5 μm.
Extended Data Fig. 4 Diagram of the optical measurement setup.
a, Experimental setup for the measurement of the polariton lattice at room temperature. A 250-fs pulse laser (370 nm center wavelength) with a repetition rate of 200 kHz was used to achieve non-resonant excitation. A reflective liquid-crystal SLM was used to generate excitation laser patterns in a Fourier imaging configuration. The PL was collected by another objective in a transmission configuration. The momentum-space images can be obtained by a Fourier imaging configuration with two achromatic tube lenses. An Andor spectrometer with a 2D EMCCD was used to measure the energy-resolved momentum-space dispersions. A pinhole at the real-space imaging plane was used to isolate the PL from other areas. A Princeton EMCCD was used to obtain the real-space image. The interference fringe was measured by a CCD camera in a Michelson interferometer. b, PL of a bare CsPbCl3 plate with a triangle pattern pumping. By sampling the PL intensity along the triangle pattern from the EMCCD, a feedback method was used to adjust the uniformity of the triangle pattern. Scalebar: 2 μm.
Extended Data Fig. 5 Characterization of the strong coupling behaviors of unpatterned samples.
a-I-IV, Angle-resolved PL dispersions of unpatterned CsPbCl3 microcavities. The dashed lines show the fitting curves based on the coupled model in Supplementary Text Section I. Due to variations in the thickness of different perovskite plates and PMMA coatings, these samples show different strong-coupling behaviors. Here, the exciton energy was extracted from the absorption spectrum in Extended Data Fig. 2 as Eex = 3.042 eV. The cavity effective mass is fitted as mcp = 0.11 meV/(µm/ps)2 for these four cavities, corresponding to a same refractive index for these perovskites. With detuning change from negative to positive (−103, −19, 97, and 193 meV from I–IV, respectively), the bending effect of the lower polariton branch demonstrates the strong coupling behavior clearly. Due to the strong absorption and large coupling strength, the upper polariton branch cannot be observed. All the lower polariton branches show negligible TE-TM splitting. b-I-IV, The corresponding Hopfield coefficients of the lower polariton branches based on the strong coupling model. On the other hand, due to the large Rabi splitting strength, the lower polariton branch can condensate with a large range of fractions of exciton and photon.
Extended Data Fig. 6 The momentum-space dispersions along the y-axis.
a and b, The simulated and experimental momentum-space dispersions of the bulk area along the y-axis (ΓM direction) of the sample in Fig. 2d of the main text, respectvely.
Extended Data Fig. 7 The momentum-space dispersions of another sample.
a and b, The PL dispersions of the bulk area along ΓM and ΓK directions, respectively. An energy gap of 14.3 meV was observed in this sample. c, The dispersion of the topological interface area along ΓK direction. The topological edge states are observed clearly, as indicated by the red arrows.
Extended Data Fig. 8 Energy-resolved polariton propagation of two waveguide samples.
a-I, The PL dispersion of the topological interface along the x-axis (K→Γ→K’ direction). A non-resonant laser (dashed red circle) was used to pump the Ω-shaped waveguide, as shown in II. A bandwidth filter (1-nm full linewidth at half maximum) is used to extract polariton PL below, within, and above the topological bandgap, as indicated by the semi-transparent rectangle in a-I. The corresponding saturated real-space propagations are illustrated in the Fig. a-III, a-IV, and a-V, respectively. Only the topological edge state within the topological bandgap in a-IV can propagate along the Ω-shaped waveguides robustly. Comparatively, the bulk state in a-III lacks eigenstates on the interface, leading to undirected diffusion. In a-V, although there are trivial edge states above the topological bandgap, the strong decay occurs when polaritons encounter 120° sharp corners due to the lack of topological protection. This is also illustrated by the normalized PL intensity in a-VI. Due to the maximum PL being in the bulk state in III, the PL intensity on the waveguide is lower than that of the edge states, as shown by the solid black line in Fig. a-VI. There are still some bulk states in a-V because we can only filter the PL signal by a bandwidth filter. It is worth noting that, different from the passive silicon-based waveguides with negligible losses, in our active perovskite microcavity, before polariton condensation, strong absorption from the perovskite gain medium impedes the long-distance propagation of polaritons. A Z-shaped waveguide in another sample also shows similar results in b. These different propagations are also proved by the time-dependent numerical simulations (described in Supplementary Text Section III and Supplementary Videos 1–3). These results prove the robust topological propagation of the edge state in our perovskite polariton system. Scale bars in (a and b): 2 μm.
Extended Data Fig. 9 Another sample for room-temperature polariton condensation of the topological edge states.
a, Real-space PL image above the condensation threshold. A triangle laser profile was used to pump the topological edge selectively. Above the condensation threshold, the system condensates at the topological interface. b, Interference of the real-space lasing image in a and its mirror image. For this sample, even with some defects and clearly noticeable inhomogeneity, the interference fringes still demonstrate the phase-locking and the long-range spatial coherence of the entire triangle topological edge. The inset shows the zoom-in image of the corner. Scale bars in (a and b): 2 μm.
Extended Data Fig. 10 Room-temperature polariton condensation of the trivial bulk states.
a, Real-space PL image below the condensation threshold. A triangle laser profile was used to pump the bulk area. The real-space image and its mirror image were symmetrically overlapped along the blue dashed line. Below the condensation threshold, only short-range interference near the symmetry axis was observed in b. c, the extracted first-order autocorrelation function g(1)(r,-r) from b. d, Real-space PL image above the condensation threshold. The condensation occurs at the ground bulk state. Because of the non-propagation character, this bulk condensations act like isolated condensates and no long-range spatial coherence of the entire triangle pumping area was observed in the interference image (e) and the extracted interference visibility (f). Scale bars in (a-f): 2 μm.
Supplementary information
Supplementary Information
Supplementary text and Figs. 1–6.
Supplementary Video 1
Time-resolved polariton propagation along the Z-shaped waveguide of an initial bulk state.
Supplementary Video 2
Time-resolved polariton propagation along the Z-shaped waveguide of an initial topological edge state (marked as blue star in Supplementary Fig. 6).
Supplementary Video 3
Time-resolved polariton propagation along the Z-shaped waveguide of an initial backscattering non-topological edge state (marked as green star in Supplementary Fig. 6).
Source data
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Raw data for plot in Fig. 1.
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Source Data Fig. 4
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Source Data Extended Data Fig. 2
Raw data for plot in Extended Data Fig. 2.
Source Data Extended Data Fig. 3
Raw data for plot in Extended Data Fig. 3.
Source Data Extended Data Fig. 5
Raw data for fitting in Extended Data Fig. 5.
Source Data Extended Data Fig. 8
Raw data for plot in Extended Data Fig. 8.
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Peng, K., Li, W., Sun, M. et al. Topological valley Hall polariton condensation. Nat. Nanotechnol. (2024). https://doi.org/10.1038/s41565-024-01674-6
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DOI: https://doi.org/10.1038/s41565-024-01674-6
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