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Spin-polarized spatially indirect excitons in a topological insulator

Nature volume 614, pages 249–255 (2023)Cite this article

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Abstract

The exciton, a bound state of an electron and a hole, is a fundamental quasiparticle induced by coherent light–matter interactions in semiconductors. When the electrons and holes are in distinct spatial locations, spatially indirect excitons are formed with a much longer lifetime and a higher condensation temperature. One of the ultimate frontiers in this field is to create long-lived excitonic topological quasiparticles by driving exciton states with topological properties, to simultaneously leverage both topological effects and correlation1,2. Here we reveal the existence of a transient excitonic topological surface state (TSS) in a topological insulator, Bi2Te3. By using time-, spin- and angle-resolved photoemission spectroscopy, we directly follow the formation of a long-lived exciton state as revealed by an intensity buildup below the bulk-TSS mixing point and an anomalous band renormalization of the continuously connected TSS in the momentum space. Such a state inherits the spin-polarization of the TSS and is spatially indirect along the z axis, as it couples photoinduced surface electrons and bulk holes in the same momentum range, which ultimately leads to an excitonic state of the TSS. These results establish Bi2Te3 as a possible candidate for the excitonic condensation of TSSs3 and, in general, opens up a new paradigm for exploring the momentum space emergence of other spatially indirect excitons, such as moiré and quantum well excitons4,5,6, and for the study of non-equilibrium many-body topological physics.

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Fig. 1: Excitons and topological states in Bi2Te3.
Fig. 2: Formation of excitons.
Fig. 3: Electron–hole dynamics.
Fig. 4: Spin character of the excitonic state.
Fig. 5: Excitonic topological state.

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Data availability

The data that support the finding of this study are available from the corresponding author upon request.

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Acknowledgements

We thank H. Tajima, Y. Lin, C. Stansbury, N. Dale, D. Eilbott, M. Huber and M. Takahashi for useful discussions. Both the experimental and theoretical parts of this work were primarily supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering Division under Contract No. DE-AC02-05CH11231 (Ultrafast Materials Science Program KC2203). R.M. acknowledges additional support from the Funai Foundation for Information Technology. K.T. acknowledges additional support from the JSPS Overseas Research Fellowship and J.E.M. acknowledges additional support from a Simons Investigatorship. T.M. was supported by JST PRESTO (JPMJPR19L9) and JST CREST (JPMJCR19T3).

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  1. Ryo Mori

    Present address: Institute for Solid State Physics, The University of Tokyo, Kashiwa, Japan

Authors and Affiliations

  1. Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA

    Ryo Mori, Samuel Ciocys, Kazuaki Takasan, Ping Ai, Kayla Currier, Joel E. Moore & Alessandra Lanzara

  2. Department of Physics, University of California, Berkeley, CA, USA

    Ryo Mori, Samuel Ciocys, Kazuaki Takasan, Ping Ai, Kayla Currier, Joel E. Moore & Alessandra Lanzara

  3. Department of Physics, The University of Tokyo, Tokyo, Japan

    Kazuaki Takasan

  4. Department of Applied Physics, The University of Tokyo, Tokyo, Japan

    Takahiro Morimoto

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Contributions

R.M. and A.L. initiated and directed this research project. R.M., P.A. and S.C. carried out the trARPES measurements. R.M., S.C. and K.C. carried out the stARPES measurements. R.M. and K.T. provided the theoretical models and calculations. T.M. and J.E.M. provided theoretical insights. R.M. analysed the ARPES data and wrote the text, with feedback from all authors.

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Correspondence to Ryo Mori or Alessandra Lanzara.

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Extended data figures and tables

Extended Data Fig. 1 Time-resolved ARPES spectra over a wide energy range.

Non-equilibrium ARPES spectrum of energy versus momentum cuts along the \(\bar{\Gamma }-\bar{{\rm{M}}}\) direction, measured at 20 K before and 0, 0.2, 0.4, 0.6, 1, 3, and 5, 10 ps after pumping from left to right. At the earliest stage (0-0.2 ps), the upper surface resonance state (SR2) is observed. Photoexcited electrons in SR2 decay fast to populate the lower surface resonance state (SR1) and bulk conduction band (CB), consistent with previous study75.

Extended Data Fig. 2 Time-resolved ARPES spectra over a wide energy range with different temperatures.

a, Non-equilibrium ARPES spectrum of energy versus momentum cuts along the \(\bar{\Gamma }-\bar{{\rm{M}}}\) direction, measured at 20 K before and 1, 2.5, 5, 10, 20, 30 ps after pumping from left to right. The white dashed-line represent the Fermi level. b, The same as panel a, but measured at 180 K.

Extended Data Fig. 3 Temperature dependence of a bulk band gap in Bi2Te3.

a, Time-resolved ARPES spectra of energy versus momentum cuts along \(\bar{\Gamma }-\bar{{\rm{M}}}\) direction for the p-type sample at 15 ps after pumping, measured at 180 K. The red bars on the top represent the integrated momentum range for the EDCs shown in b—e. Four energy levels are defined here; the energy level of the Dirac point (EDP), the bulk valence band maximum (EV BM), the bulk conduction band local minimum at \(\bar{\Gamma }\) point (ECBG), and the bulk indirect band gap (EIDG). The energy levels are relative energy to the EDP. Note that the intensity in the black-dashed squared area is enhanced for better visuality. b,c, Integrated EDCs around \(\bar{\Gamma }\) point, measured at 20 K (red), 80 K (blue), 180 K (green), and 200 K (orange). The weak signals from the bulk conduction band local minimum around \(\bar{\Gamma }\) point (see the black dashed square in b) are enlarged in c. d, Integrated EDCs around the bulk valence band maximum. Each color of EDCs corresponds to b,c. e Extracted values of ECBG, EV BM, and EIDG for each temperature. f, The schematics of the temperature dependence of the bulk structure in Bi2Te3. When the temperature increases, only the energy level of the conduction band minimum (ECBM) decreases, and the direct band gap (EDG) shrinks (see the red dashed line).

Extended Data Fig. 4 Bulk conduction bands.

a, ARPES spectrum along \(\bar{\Gamma }-\bar{{\rm{M}}}\) direction for the n-type sample, measured at 40 K (left). The red dots in ARPES spectrum represent the peaks position extracted from the energy distribution curves (EDCs) from k1 to k2 and the black line represents the extracted band dispersion, corresponding to the bulk conduction band (CB). b, The EDC at the \(k{\prime} \) (see the dashed-line in panel a) where the both topological surface state (TSS) and CB are observed for the n- (top) and the p-type samples (bottom). The p-type’s EDC is extracted from non-equilibrium ARPES spectrum measured at 20 K, integrated over 0.2-1.6 ps of delay time (for better stats). c,d, EDCs for the n-type (c) and the p-type (d). The blue and red marks in right panel show the peaks position of the topological surface state and the bulk conduction band, respectively. e, Comparison of the bulk conduction bands between the n- and p-type samples. Note that energy levels are plotted with respect to the Dirac point energy (EDP) for a direct comparison. The error bars in a,e represent the uncertainties of peak positions from Lorentzian fits.

Extended Data Fig. 5 Two distinct energy levels in EDCs.

a, Non-equilibrium ARPES spectrum of energy versus momentum cut measured at 20 K with EDCs at kbuildup. The red horizontal marks represent the estimated peak positions for bulk (CB) and exciton buildup (EX). b, Energy distribution curves (EDCs) at various delay times at 20 K at kbuildup (see the blue solid line in panel (a)). From bottom to top, each EDC corresponds to each delay time with an increment of 0.4 ps. The dashed-lines are guide to the eye for the estimated peak positions.

Extended Data Fig. 6 Temperature dependence of buildup.

a, The intensity buildup across the various temperature. From left to right, the measurement temperature is 20, 40, 80, 90, 140, and 180 K. The data are taken at the delay times when the bulk states are relaxed for each temperature. b, Temperature dependence of intensity of the buildup. Note the intensity is normalized by the intensity of the proximate TSS. The error bars are estimated by absolute maximum variations of the integration. c, Transient electronic temperature of the intensity buildup for each measurement temperature. The black horizontal line indicates 160 K (~ 14 meV). The error bars are from the uncertainty in the fitting and experimental resolution.

Extended Data Fig. 7 Fine delay scan at 180 K.

a, Non-equilibrium ARPES spectrum of energy versus momentum cut measured at 180 K. b, Energy distribution curves (EDCs) at ten representative delay times at 180 K, obtained by integration over the momentum range around kbuildup. From bottom to top, each unlabeled EDC corresponds to each delay time with an increment of 0.4 ps. The dashed-lines are guide to the eye for the estimated peak positions.

Extended Data Fig. 8 In-plane momentum- and real-space distribution of the Wannier-exciton in Bi2Te3.

a, In-plane constant energy map at the energy level of the Wannier-exciton signature (E − EDP = 0.305 eV) obtained at the delay time t = 20 ps. The solid black line represent the surface projected BZ. The data are symmetrized assuming six-fold symmetry and focusing only on the intensity buildup. b, 2D Fourier transform of the momentum-resolved photoemission intensity I(kx,ky) recovers the real-space image I(rx,ry), featuring the electron density distribution of the excitonic wavefunction. The high frequency oscillations reflect the hexagonal lattice structure.

Extended Data Fig. 9 Circular dichroism.

a, Sum of non-equilibrium ARPES spectrum of energy versus momentum cut along \(\bar{\Gamma }-\bar{{\rm{M}}}\) measured at time delay 2 ps with the left (CL) and right circularly polarized photons (CR). The color scale in the gray dashed area is enhanced. The black dashed lines are guide for the eye, representing the bulk conduction band and the TSS-bulk continuum. b,c, Circular dichroism (CD) for for delay time 2 ps (b) and 10 ps (c), obtained by (CL − CR)/(CL + CR). The black arrow indicates the location of the bulk state. The black dashed lines in b are guide for the eye, representing the bulk conduction band and the TSS-bulk continuum. The black circle in panel c indicates the observed intensity buildup. d,e, The sum spectrum (CL + CR) (d) and the CD spectrum (CL − CR)/(CL + CR) (e), focusing on the bulk conduction band and the bulk-TSS connection (see the gray dashed square in panel a at time delay 2 ps. The black dashed lines are guide for the eye, representing the bulk conduction band and the TSS-bulk continuum. f, The CD spectra at time delay 10 ps with enhanced color scale, focusing on the exciton intensity buildup.

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Supplementary Figs. 1–4, equations (1)–(13) and References.

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Mori, R., Ciocys, S., Takasan, K. et al. Spin-polarized spatially indirect excitons in a topological insulator. Nature 614, 249–255 (2023). https://doi.org/10.1038/s41586-022-05567-3

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