Abstract
Correlated topological materials often maintain a delicate balance among physical symmetries. Many topological orders are symmetry protected, whereas most correlated phenomena arise from spontaneous symmetry breaking. Cases where symmetry breaking induces a non-trivial topological phase are rare. Here we demonstrate the presence of two such phases in Ta2Pd3Te5, where Coulomb interactions form excitons that condense below 100 K, one with zero and the other with finite momentum. We observed a full spectral bulk gap, which stems from exciton condensation. This topological excitonic insulator state spontaneously breaks mirror symmetries but involves a weak structural coupling. Scanning tunnelling microscopy shows gapless boundary modes in the bulk insulating phase. Their magnetic field response, together with theoretical modelling, indicates a topological origin. These observations establish Ta2Pd3Te5 as a topological excitonic insulator in a three-dimensional crystal. Thus, our results manifest a unique sequence of topological exciton condensations in a bulk crystal, offering exciting opportunities to study critical behaviour and excitations.
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Acknowledgements
M.Z.H.’s group at Princeton University acknowledges primary support from the US Department of Energy (DOE), Office of Science, under the Basic Energy Sciences (DOE-BES) programme (grant no. DOE/BES DE-FG-02- 05ER46200), for the advanced spectroscopic measurements and theoretical including ARPES, and the National Quantum Information Science Research Centers, the Quantum Science Center and Princeton University; ARPES, STM and transport instrumentation support from the Gordon and Betty Moore Foundation (grant no. GBMF9461) and Princeton University; and support from the US DOE under the Basic Energy Sciences (DOE-BES) programme (grant no. DOE/BES DE-FG-02- 05ER46200) for the theoretical work and extensive sample characterization. This research utilized the Stanford Synchrotron Radiation Lightsource (SSRL) at SLAC National Accelerator Laboratory, supported by the US DOE, Office of Science, Office of Basic Energy Sciences under contract no. DE-AC02-76SF00515. It also used Beamline 21-ID-1 (ESM-ARPES) at the National Synchrotron Light Source II (NSLS-II), a DOE Office of Science User Facility operated by Brookhaven National Laboratory under Contract No. DE-SC0012704. Additional support was provided by the Advanced Light Source (ALS), a DOE Office of Science User Facility operated under contract no. DE-AC02-05CH11231. We acknowledge D. Lu and M. Hashimoto for their expert support at Beamline 5-2 of SSRL, SLAC National Accelerator Laboratory, and E. Vescovo and T. Yilmaz for their technical assistance at Beamline 21-ID-1 (ESM-ARPES) of NSLS-II. We also thank C. Jozwiak, A. Bostwick and E. Rotenberg for their support at Beamline 7.0.2 of the ALS. Crystal growth at Beijing Institute of Technology is supported by the National Key Research and Development Program of China (grant nos. 2020YFA0308800 and 2022YFA1403400), the National Science Foundation of China (grant no. 92065109), the Beijing Natural Science Foundation (grant no. Z210006) and the Beijing National Laboratory for Condensed Matter Physics (grant no. 2023BNLCMPKF007). L.B. is supported by DOE-BES (award no. DE-SC0002613). The National High Magnetic Field Laboratory acknowledges support from a US NSF cooperative agreement (grant no. DMR-DMR-2128556) and the state of Florida. We thank T. Murphy, G. Jones, L. Jiao and R. Nowell at the National High Magnetic Field Laboratory for technical support. T.N. acknowledges support from the Swiss National Science Foundation through a Consolidator Grant (iTQC, TMCG-2_213805). Z.W. thanks the Analysis and Testing Center at BIT for assistance with facility support. Y.Y.P. is grateful for financial support from the National Natural Science Foundation of China (grant no. 11974029). G.C. and N.Y. acknowledge the use of Princeton’s Imaging and Analysis Center, which is partially supported by the Princeton Center for Complex Materials, a National Science Foundation (NSF)-MRSEC programme (DMR-2011750). This research used resources of the Advanced Light Source, which is a DOE Office of Science User Facility (contract no. DE-AC02-05CH11231). S.-B.Z. is supported by the start-up fund at HFNL, the Innovation Program for Quantum Science and Technology (grant no. 2021ZD0302800) and the Anhui Initiative in Quantum Information Technologies (grant no. AHY170000).
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M.S.H. conceived the project. The STM experiments were performed by M.S.H. and Y.-X.J. Transport experiments were performed by M.S.H. and Q.Z. under consultation with L.B. The ARPES experiments were performed by Z.-J.C., T.A.C. and B.K. with the help of J.D.D., M.T., J.D., E.V. and A.R. S.-B.Z. performed the tight-binding calculations under consultation with T.N. X.L. performed the first-principles calculations under consultation with T.N. The crystals were grown by H.W., J.L., Y.Y. and Z.W. G.C. and N.Y. performed the TEM. X.Z. and Y.P. performed X-ray measurements. M.L., X.P.Y., J.Z. and J.-X.Y. helped with the measurements. A.K. helped with interpreting the data. M.S.H., Z.-J.C., T.A.C., T.N., L.B. and M.Z.H. developed the figures and wrote the paper. M.Z.H. supervised the project. All authors discussed and interpreted the results and participated in drawing the conclusions.
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Extended data
Extended Data Fig. 1 Selected area electron diffraction patterns detecting no lattice instabilities near T = 100 K.
a, Atomic-resolution image of the (010) surface of a lamella captured by scanning transmission electron microscopy, demonstrating a consistent atomic arrangement when compared to pristine Ta2Pd3Te5 (010) crystallographic structure. b, Selected area electron diffraction patterns obtained from the focused-ion-beam cut lamella at T = 290 K (top) and 90 K (bottom). The patterns exhibit identical crystal lattice at both temperatures, detecting no structural phase change in this temperature range. c, Atomic-resolution scanning transmission electron microscopy image of the (001) surface, revealing a consistent atom arrangement when compared to pristine Ta2Pd3Te5 (001). d, Selected area electron diffraction patterns acquired from the focused-ion-beam cut lamella at T = 290 K (top) and 90 K (bottom). Akin to panel b, the patterns demonstrate the same crystal lattice at both temperatures. The temperature-dependent selected area electron diffraction patterns detect no structural phase transition around 100 K.
Extended Data Fig. 2 Structure and phase characterization of Ta2Pd3Te5.
a, Atomic resolution image of the side surface of Ta2Pd3Te5 (that is, 010 plane), obtained through scanning transmission electron microscopy, displaying a consistent atomic arrangement when compared to pristine Ta2Pd3Te5. b–i, Elemental mappings of the side surface utilizing an energy dispersive X-ray detector. The mappings demonstrate the unperturbed atomic layers, highlighting the structural integrity and composition of Ta2Pd3Te5.
Extended Data Fig. 3 X-ray diffraction measurements on Ta2Pd3Te5 detecting no structural phase transition as a function of temperature.
a, X-ray diffraction pattern measured at the same sample position for different temperatures ranging from 300 K to 20 K. b, Maps along the H-L direction obtained by summing over K= [−2.5, 3.5] and measured at four temperatures. c, Maps along H-L obtained by taking a slice at K = [0.5,1.5] measured at four temperatures. d, Maps along H-K obtained by summing over L = [−7.5, 20.5] and measured at four temperatures. e, Maps along H-K obtained by taking a slice at L = [1.5, 2.5]. Notably, there is no emergence of any new or additional peak at low temperatures. X-ray diffraction measurements consistently exhibit a good agreement with the Pnma crystal structure at all the measured temperatures.
Extended Data Fig. 4 Determination of the energy gap from tunneling spectroscopy.
a, Averaged dI/dV spectrum acquired by tunneling into the bc plane of clean Ta2Pd3Te5 at T = 5 K. The voltage interval \([{V}_{1},{V}_{2}]\) is used to calculate the noise floor, σ. The dashed red line represents \(\varGamma =2.36\sigma\), which corresponds to the instrumental resolution of the dI/dV signal. \({V}_{a}\) and \({V}_{b}\) are the solutions of the equation \({\rm{d}}I/{\rm{d}}V=\varGamma\). The spectroscopic energy gap is calculated as \(\varDelta =e{V}_{a}\mbox{--}e{V}_{b}\), resulting in Δ ≃ 70 meV. b, Magnified view of panel a, focusing on the gapped region in the averaged dI/dV spectrum.
Extended Data Fig. 5 Observation of time-reversal-symmetry-protected edge states for different edge configurations.
a, dI/dV maps acquired at different bias voltages (corresponding topography is shown in the bottom panel) around a monolayer step edge parallel to the c-axis measured at T = 5 K. The height profile perpendicular to the c-axis is also displayed. The dI/dV map obtained within the energy gap (V = 0 mV) reveals a pronounced edge state, whereas at V = 210 mV, the edge state is suppressed. b, Tunneling spectra acquired at locations away from the step edge and on the step edge measured under various magnetic fields. The orange and violet curves represent the differential spectra obtained at the step edge and away from it, respectively. The corresponding spatial locations where the spectra are acquired are marked with color-coded dots on the topographic image in panel a. Spectra at different magnetic fields were collected at the same locations and are vertically offset for clarity. Dashed horizontal lines mark the zero dI/dV for different fields. c, dI/dV maps acquired at different bias voltages (corresponding topography is shown in the bottom panel) around a four-layer step edge parallel to the b-axis direction. The height profile perpendicular to the b-axis is also shown. The dI/dV map obtained within the energy gap (V = 0 mV) reveals a pronounced edge state, whereas at V = 210 mV, the edge state is suppressed. d, Tunneling spectra acquired at locations away from the step edge and on the step edge measured under various magnetic fields. The orange and violet curves represent the differential spectra taken at the step edge and away from it, respectively. The corresponding spatial locations where the spectra are acquired are marked with color-coded dots on the topographic image in panel a. Spectra at different magnetic fields were taken at the same locations and are vertically offset for clarity. Dashed horizontal lines mark the zero dI/dV for different fields. Tunneling junction set-up: Vset = 300 mV, Iset = 0.5 nA, Vmod = 2 mV.
Extended Data Fig. 6 Magnetic field tunability of the wavevector of the translational symmetry breaking order.
a, Atomically resolved topographic image of a clean Ta2Pd3Te5 (100) surface acquired at T = 5 K. Inset shows the corresponding Fourier transform image displaying well-defined Bragg peaks (purple circles). b, Topographic image of the same region presented in panel a, acquired at T = 4.2 K and B = 0 T, revealing a pronounced translational symmetry breaking order. Inset: Fourier transform image displaying well-defined superlattice peaks (orange circles) alongside the Bragg peaks (purple circles). The extracted wavevector is \({Q}_{{\rm{exc}}}=\left[\right.\pm \left(-0.43{c}^{* }+0.035{b}^{* }\right),\)\(\pm \left(0.57{c}^{* }+0.035{b}^{* }\right)\left.\right]\). c–e, Topographic images from the same location but acquired at magnetic fields of 2 T, 4 T, and 6 T, respectively, highlighting a change in the translational symmetry breaking ordering pattern upon increasing the magnetic field. The Fourier transform images shown in the inset reveal a gradually evolving Qexc where Qexc changes to [\(\pm \left(-0.44{c}^{* }+0.051{b}^{* }\right),\pm \left(0.56{c}^{* }+0.051{b}^{* }\right)\)] at 2 T, [\(\pm \left(-0.47{c}^{* }+0.06{b}^{* }\right),\)\(\pm \left(0.53{c}^{* }+0.06{b}^{* }\right)\)] at 4 T, and \(\pm \left(0.5{c}^{* }+0.07{b}^{* }\right)\)] at 6 T. f, Polar plot summarizing the magnetic field tunability of Qexc. Starting from being incommensurate along both b- and c-axes at \(B=0\) T, Qexc evolves continuously and becomes commensurate along the c-axis at \(B=6\) T. Tunneling junction set-up: Vset = 300 mV, Iset = 0.5 nA.
Extended Data Fig. 7 Low-energy band structure of monolayer Ta2Pd3Te5 obtained from first-principles calculations.
Monolayer Ta2Pd3Te5 exhibits semimetallic band structure.
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Hossain, M.S., Cheng, ZJ., Jiang, YX. et al. Topological excitonic insulator with tunable momentum order. Nat. Phys. 21, 1250–1259 (2025). https://doi.org/10.1038/s41567-025-02917-6
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DOI: https://doi.org/10.1038/s41567-025-02917-6
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