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Boundary modes of a charge density wave state in a topological material

Abstract

Charge density waves appear in numerous condensed matter platforms ranging from high-temperature superconductors to quantum Hall systems. Despite such ubiquity, there has been a lack of direct experimental study of boundary states that can uniquely stem from the charge order. Here we directly visualize the bulk and boundary phenomenology of the charge density wave in a topological material, Ta2Se8I, using scanning tunnelling microscopy. At a monolayer step edge, we demonstrate the presence of an in-gap boundary mode persisting up to the charge ordering temperature with modulations along the edge that match the charge density wave wavevector along the edge. Furthermore, these results manifesting the presence of an edge state challenge the existing axion insulator interpretation of the charge-ordered phase in this compound.

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Fig. 1: Electronic nature of charge density wave in Ta2Se8I.
Fig. 2: Observation of an edge state within the charge density wave gap.
Fig. 3: Temperature dependence of the charge density wave and its in-gap edge state.
Fig. 4: Correspondence between the periodicity of the edge dI/dV modulations and charge density wave wavelength projected along the edge.
Fig. 5: Gapless edge mode connecting the gapped bulk (and surface) conduction and valence bands in energy and phase.

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All data needed to evaluate the conclusions in the paper are present in the paper. Additional data are available from the corresponding authors upon reasonable request. Source data are provided with this paper.

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Acknowledgements

The M.Z.H. group acknowledges primary support from the US Department of Energy, Office of Science, National Quantum Information Science Research Centers, Quantum Science Center (at ORNL) and Princeton University; scanning tunneling microscopy instrumentation support from the Gordon and Betty Moore Foundation (GBMF9461) and the theory work; and support from the US DOE under the Basic Energy Sciences programme (grant number DOE/BES DE-FG-02-05ER46200) for the theory and sample characterization work including photoemission spectroscopy. T.N. acknowledges supports from the European Union’s Horizon 2020 research and innovation programme (ERC-StG-Neupert-757867-PARATOP) and from the Swiss National Science Foundation through a Consolidator Grant (iTQC, TMCG-2_213805). Work at Nanyang Technological University was supported by the National Research Foundation, Singapore, under its Fellowship Award (NRF-NRFF13-2021-0010), the Agency for Science, Technology and Research (A*STAR) under its Manufacturing, Trade and Connectivity (MTC) Individual Research Grant (IRG) (Grant No.: M23M6c0100), and the Nanyang Assistant Professorship grant (NTU-SUG). Crystal growth at Beijing Institute of Technology is supported by National Science Foundation of China (NSFC) (grant nos 92065109, 12321004 and 12234003), the National Key R&D Program of China (grant nos 2020YFA0308800 and 2022YFA1403400) and the Beijing Natural Science Foundation (grant no. Z210006). Z.W. thanks the Analysis and Testing Center at BIT for assistance through facility support. S.-B.Z. is supported by the Innovation Program for Quantum Science and Technology (grant no. 2021ZD0302800) and the Anhui Initiative in Quantum Information Technologies (grant no. AHY170000). Crystal growth at Max Planck Institute for Chemical Physics of Solids is funded by European Research Council (ERC) advanced grant no. 742068 (‘TOPMAT’), the Deutsche Forschungsgemeinschaft (DFG) under SFB 1143 (project no. 247310070) and the Würzburg-Dresden Cluster of Excellence on Complexity and Topology in Quantum Matter – ct.qmat (EXC 2147, project no. 39085490). G. Cheng 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). X.L. acknowledges support from the National Key R&D Program of China (grant no. 2022YFA1403700).

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STM experiments were performed by M.L. and M.S.H. in consultation with M.Z.H. Crystal growth was carried out by S.N.G., N.K., C.S., Z.W. and Y.L under supervision of Y.Y. and C.F. Transmission electron microscopy measurements were performed by G.C. and N.Y. ARPES experiments were performed by Z.-J.C. in consultation with M.S.H. and M.Z.H. Theoretical modelling and calculations uncovering the underlying topology of the boundary mode were carried out by S.-B.Z. and X.L. under supervision of T.N. Writing of the manuscript and figure production were undertaken by M.S.H., M.L., S.-B.Z., T.N., Z.-J.C. and M.Z.H. All the authors contributed to the discussion of the results, interpretation and conclusion.

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Correspondence to Md Shafayat Hossain or M. Zahid Hasan.

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Litskevich, M., Hossain, M.S., Zhang, SB. et al. Boundary modes of a charge density wave state in a topological material. Nat. Phys. (2024). https://doi.org/10.1038/s41567-024-02469-1

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