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Layer-by-layer disentanglement of Bloch states

Nature Physics (2023)Cite this article

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Abstract

Layer-by-layer material engineering has produced interesting quantum phenomena such as interfacial superconductivity and the quantum anomalous Hall effect. However, probing electronic states layer by layer remains challenging. This is exemplified by the difficulty in understanding the layer origins of topological electronic states in magnetic topological insulators. Here we report a layer-encoded frequency-domain photoemission experiment on the magnetic topological insulator (MnBi2Te4)(Bi2Te3) that characterizes the origins of its electronic states. Infrared laser excitations launch coherent lattice vibrations with the layer index encoded by the vibration frequency. Photoemission spectroscopy then tracks the electron dynamics, where the layer information is carried in the frequency domain. This layer–frequency correspondence shows wavefunction relocation of the topological surface state from the top magnetic layer into the buried second layer, reconciling the controversy over the vanishing broken-symmetry energy gap in (MnBi2Te4)(Bi2Te3) and its related compounds. The layer–frequency correspondence can be harnessed to disentangle electronic states layer by layer in a broad class of van der Waals superlattices.

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Fig. 1: Experimental scheme and the electronic band structure of an (MBT)(BT) superlattice.
Fig. 2: Coherent response of the TSS to phonon oscillations on the BT termination.
Fig. 3: Coherent response on the MBT termination.
Fig. 4: Schemes of layer-by-layer disentanglement of Bloch states.

Data availability

Source data are provided with this paper. All other data that support the plots and other findings of this study are available from the corresponding authors upon reasonable request.

References

  1. Liu, C. et al. Robust axion insulator and Chern insulator phases in a two-dimensional antiferromagnetic topological insulator. Nat. Mater. 19, 522–527 (2020).

    Article  ADS  Google Scholar 

  2. Deng, Y. et al. Quantum anomalous Hall effect in intrinsic magnetic topological insulator MnBi2Te4. Science 367, 895–900 (2020).

    Article  ADS  Google Scholar 

  3. Klimovskikh, I. I. et al. Tunable 3D/2D magnetism in the (MnBi2Te4)(Bi2Te3)m topological insulators family. npj Quantum Mater. 5, 54 (2020).

    Article  ADS  Google Scholar 

  4. Hao, Y.-J. et al. Gapless surface Dirac cone in antiferromagnetic topological insulator MnBi2Te4. Phys. Rev. X 9, 041038 (2019).

    Google Scholar 

  5. Chen, Y. J. et al. Topological electronic structure and its temperature evolution in antiferromagnetic topological insulator MnBi2Te4. Phys. Rev. X 9, 041040 (2019).

    Google Scholar 

  6. Nevola, D. et al. Coexistence of surface ferromagnetism and a gapless topological state in MnBi2Te4. Phys. Rev. Lett. 125, 117205 (2020).

    Article  ADS  Google Scholar 

  7. Otrokov, M. M. et al. Prediction and observation of an antiferromagnetic topological insulator. Nature 576, 416–422 (2019).

    Article  ADS  Google Scholar 

  8. Shikin, A. M. et al. Sample-dependent Dirac-point gap in MnBi2Te4 and its response to applied surface charge: a combined photoemission and ab initio study. Phys. Rev. B 104, 115168 (2021).

    Article  ADS  Google Scholar 

  9. Li, H. et al. Dirac surface states in intrinsic magnetic topological insulators EuSn2As2 and MnBi2nTe3n+1. Phys. Rev. X 9, 041039 (2019).

    Google Scholar 

  10. Vidal, R. C. et al. Orbital complexity in intrinsic magnetic topological insulators MnBi4Te7and MnBi6Te10. Phys. Rev. Lett. 126, 176403 (2021).

    Article  ADS  Google Scholar 

  11. Wu, X. et al. Distinct topological surface states on the two terminations of MnBi4Te7. Phys. Rev. X 10, 031013 (2020).

    Google Scholar 

  12. Hu, C. et al. A van der Waals antiferromagnetic topological insulator with weak interlayer magnetic coupling. Nat. Commun. 11, 97 (2020).

    Article  ADS  Google Scholar 

  13. Yuan, Y. et al. Electronic states and magnetic response of MnBi2Te4 by scanning tunneling microscopy and spectroscopy. Nano Lett. 20, 3271–3277 (2020).

    Article  ADS  Google Scholar 

  14. Hein, P. et al. Mode-resolved reciprocal space mapping of electron–phonon interaction in the Weyl semimetal candidate Td-WTe2. Nat. Commun. 11, 2613 (2020).

    Article  ADS  Google Scholar 

  15. Gerber, S. et al. Femtosecond electron–phonon lock-in by photoemission and X-ray free-electron laser. Science 357, 71–75 (2017).

    Article  ADS  Google Scholar 

  16. Suzuki, T. et al. Detecting electron–phonon coupling during photoinduced phase transition. Phys. Rev. B 103, L121105 (2021).

    Article  ADS  Google Scholar 

  17. Yan, C. et al. An integrated quantum material testbed with multi-resolution photoemission spectroscopy. Rev. Sci. Instrum. 92, 113907 (2021).

    Article  ADS  Google Scholar 

  18. Cho, Y. et al. Phonon modes and Raman signatures of MnBi2nTe3n+1 (n = 1, 2, 3, 4) magnetic topological heterostructures. Phys. Rev. Res. 4, 013108 (2022).

    Article  Google Scholar 

  19. Zeiger, H. J. et al. Theory for displacive excitation of coherent phonons. Phys. Rev. B 45, 768–778 (1992).

    Article  ADS  Google Scholar 

  20. De Giovannini, U., Hübener, H., Sato, S. A. & Rubio, A. Direct measurement of electron–phonon coupling with time-resolved ARPES. Phys. Rev. Lett. 125, 136401 (2020).

    Article  ADS  Google Scholar 

  21. Shahil, K. M. F., Hossain, M. Z., Teweldebrhan, D. & Balandin, A. A. Crystal symmetry breaking in few-quintuple Bi2Te3 films: applications in nanometrology of topological insulators. Appl. Phys. Lett. 96, 153103 (2010).

    Article  ADS  Google Scholar 

  22. Jahangirli, Z. A. et al. Electronic structure and dielectric function of Mn–Bi–Te layered compounds. J. Vac. Sci. Technol. B 37, 062910 (2019).

    Article  Google Scholar 

  23. He, R. et al. Observation of infrared-active modes in Raman scattering from topological insulator nanoplates. Nanotechnology 23, 455703 (2012).

    Article  ADS  Google Scholar 

  24. Khan, F. S. & Allen, P. B. Deformation potentials and electron–phonon scattering: two new theorems. Phys. Rev. B 29, 3341–3349 (1984).

    Article  ADS  Google Scholar 

  25. Li, J. J., Chen, J., Reis, D. A., Fahy, S. & Merlin, R. Optical probing of ultrafast electronic decay in Bi and Sb with slow phonons. Phys. Rev. Lett. 110, 047401 (2013).

    Article  ADS  Google Scholar 

  26. Yang, S.-L. et al. Superconducting graphene sheets in CaC6 enabled by phonon-mediated interband interactions. Nat. Commun. 5, 3493 (2014).

    Article  ADS  Google Scholar 

  27. Lee, W. S., Johnston, S., Devereaux, T. P. & Shen, Z.-X. Aspects of electron–phonon self-energy revealed from angle-resolved photoemission spectroscopy. Phys. Rev. B 75, 195116 (2007).

    Article  ADS  Google Scholar 

  28. Yang, S.-L. et al. Inequivalence of single-particle and population lifetimes in a cuprate superconductor. Phys. Rev. Lett. 114, 247001 (2015).

    Article  ADS  Google Scholar 

  29. Shikin, A. M. et al. Nature of the Dirac gap modulation and surface magnetic interaction in axion antiferromagnetic topological insulator MnBi2Te4. Sci. Rep. 10, 13226 (2020).

    Article  ADS  Google Scholar 

  30. Sitnicka, J. et al. Systemic consequences of disorder in magnetically self-organized topological MnBi2Te4 /(Bi2Te3)n superlattices. 2D Mater. 9, 015026 (2022).

    Article  Google Scholar 

  31. Guo, J. et al. Coexisting ferromagnetic–antiferromagnetic phases and manipulation in a magnetic topological insulator MnBi4Te7. J. Phys. Chem. C 126, 13884–13893 (2022).

  32. Ge, W. et al. Direct visualization of surface spin-flip transition in MnBi4Te7. Phys. Rev. Lett. 129, 107204 (2022).

    Article  ADS  Google Scholar 

  33. Ma, X.-M. et al. Hybridization-induced gapped and gapless states on the surface of magnetic topological insulators. Phys. Rev. B 102, 245136 (2020).

    Article  ADS  Google Scholar 

  34. Geim, A. K. & Grigorieva, I. V. Van der Waals heterostructures. Nature 499, 419–425 (2013).

    Article  Google Scholar 

  35. Mak, K. F. & Shan, J. Semiconductor moiré materials. Nat. Nanotechnol. 17, 686–695 (2022).

    Article  ADS  Google Scholar 

  36. Island, J. O. et al. Spin–orbit-driven band inversion in bilayer graphene by the van der Waals proximity effect. Nature 571, 85–89 (2019).

    Article  ADS  Google Scholar 

  37. Kezilebieke, S. et al. Moiré-enabled topological superconductivity. Nano Lett. 22, 328–333 (2022).

    Article  ADS  Google Scholar 

  38. Can, O. et al. High-temperature topological superconductivity in twisted double-layer copper oxides. Nat. Phys. 17, 519–524 (2021).

    Article  Google Scholar 

  39. Guan, Y. D. et al. Ferromagnetic MnBi4Te7 obtained with low-concentration Sb doping: a promising platform for exploring topological quantum states. Phys. Rev. Mater. 6, 054203 (2022).

    Article  Google Scholar 

  40. Kresse, G. & Furthmüller, J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput. Mater. Sci. 6, 15–50 (1996).

    Article  Google Scholar 

  41. Kresse, G. & Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169–11186 (1996).

    Article  ADS  Google Scholar 

  42. Blöchl, P. E. Projector augmented-wave method. Phys. Rev. B 50, 17953–17979 (1994).

    Article  ADS  Google Scholar 

  43. Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996).

    Article  ADS  Google Scholar 

  44. Grimme, S., Antony, J., Ehrlich, S. & Krieg, H. A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu. J. Chem. Phys. 132, 154104 (2010).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We acknowledge very helpful discussions with J. Sobota and P. Kirchmann from SLAC National Accelerator Laboratory, and with S. King, J. Park, P. Littlewood and S. Guha from the University of Chicago. The optimization of the static µ-ARPES set-up was partially supported by the US National Science Foundation (NSF) through grant no. DMR-2145373. The trARPES work was supported by the US Department of Energy (grant no. DE-SC0022960). The financial support for a part of sample preparation by S.H.L. was provided by the NSF through the Penn State 2D Crystal Consortium-Materials Innovation Platform (2DCC-MIP) under NSF cooperative agreement DMR-2039351. The sample synthesis efforts by Y.G. were supported by the US Department of Energy under grant DE-SC0019068. C.L. and R.M. acknowledge support from the Penn State MRSEC Center for Nanoscale Science through NSF grant no. DMR-2011839. B.Y. acknowledges financial support by the European Research Council under the European Union’s Horizon 2020 research and innovation programme (grant no. 815869).

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Author notes

  1. Sebastian Fernandez-Mulligan

    Present address: Department of History, Yale University, New Haven, CT, USA

  2. These authors contributed equally: Woojoo Lee, Sebastian Fernandez-Mulligan.

Authors and Affiliations

  1. Pritzker School of Molecular Engineering, The University of Chicago, Chicago, IL, USA

    Woojoo Lee, Sebastian Fernandez-Mulligan, Chenhui Yan & Shuolong Yang

  2. Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, Israel

    Hengxin Tan & Binghai Yan

  3. Department of Physics, Pennsylvania State University, University Park, PA, USA

    Yingdong Guan, Seng Huat Lee, Ruobing Mei, Chaoxing Liu & Zhiqiang Mao

  4. 2D Crystal Consortium, Materials Research Institute, Pennsylvania State University, University Park, PA, USA

    Seng Huat Lee

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Contributions

W.L., S.F.-M., C.Y. and S.Y. conducted the µ-ARPES and trARPES measurements. Y.G., S.H.L. and Z.M. grew the (MnBi2Te4)(Bi2Te3) samples. H.T. and B.Y. performed first-principles calculations with input from R.M. and C.L. W.L., S.F.-M. and S.Y. wrote the manuscript with input from all co-authors. S.Y. conceived the experiment.

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Correspondence to Shuolong Yang.

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Lee, W., Fernandez-Mulligan, S., Tan, H. et al. Layer-by-layer disentanglement of Bloch states. Nat. Phys. (2023). https://doi.org/10.1038/s41567-023-02008-4

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