Abstract
Room-temperature realization of macroscopic quantum phases is one of the major pursuits in fundamental physics1,2. The quantum spin Hall phase3,4,5,6 is a topological quantum phase that features a two-dimensional insulating bulk and a helical edge state. Here we use vector magnetic field and variable temperature based scanning tunnelling microscopy to provide micro-spectroscopic evidence for a room-temperature quantum spin Hall edge state on the surface of the higher-order topological insulator Bi4Br4. We find that the atomically resolved lattice exhibits a large insulating gap of over 200 meV, and an atomically sharp monolayer step edge hosts an in-gap gapless state, suggesting topological bulk–boundary correspondence. An external magnetic field can gap the edge state, consistent with the time-reversal symmetry protection inherent in the underlying band topology. We further identify the geometrical hybridization of such edge states, which not only supports the Z2 topology of the quantum spin Hall state but also visualizes the building blocks of the higher-order topological insulator phase. Our results further encourage the exploration of high-temperature transport quantization of the putative topological phase reported here.
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The data that support the findings of this study are available from the corresponding authors upon reasonable request.
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Acknowledgements
M.Z.H. acknowledges support from the US Department of Energy, Office of Science, National Quantum Information Science Research Centers, Quantum Science Center and Princeton University. M.Z.H. acknowledges visiting scientist support at Berkeley Lab (Lawrence Berkeley National Laboratory) during the early phases of this work. Theoretical and STM works at Princeton University was supported by the Gordon and Betty Moore Foundation (GBMF9461; M.Z.H.). The theoretical work including ARPES were supported by the US DOE under the Basic Energy Sciences program (grant number DOE/BES DE-FG-02-05ER46200; M.Z.H.). We further acknowledge use of Princeton’s Imaging and Analysis Center, which is partially supported by the Princeton Center for Complex Materials, a National Science Foundation Materials Research Science and Engineering Center (DMR-2011750). L.B. is supported by DOE-BES through award DE-SC0002613. C.Y. and F.Z. acknowledge the Texas Advanced Computing Center (TACC) for providing resources that have contributed to the research results reported in this work. The theoretical and computational work at University of Texas at Dallas was supported by the National Science Foundation under grant nos. DMR-1921581 (through the DMREF program), DMR-1945351 (through the CAREER program) and DMR-2105139 (through the CMP program). F.Z. also acknowledges support from the Army Research Office under grant no. W911NF-18-1-0416. T.N. acknowledges support from the European Union’s Horizon 2020 research and innovation programme (ERC-StG-Neupert-757867-PARATOP). T.-R.C. was supported by the Young Scholar Fellowship Program under a MOST grant for the Columbus Program, MOST111-2636-M-006-014, the Higher Education Sprout Project, Ministry of Education to the Headquarters of University Advancement at the National Cheng Kung University (NCKU), the National Center for Theoretical Sciences (Taiwan). Crystal growth is funded by the National Key Research and Development Program of China (2020YFA0308800), the National Science Foundation of China (NSFC) (Grants No. 92065109, No. 11734003, No. 12061131002), Y.Yao is supported the Strategic Priority Research Program of Chinese Academy of Sciences (XDB30000000). The work in Peking University was supported by CAS Interdisciplinary Innovation Team, the strategic Priority Research Program of Chinese Academy of Sciences, Grant No. XDB28000000 and the National Natural Science Foundation of China No. 12141002. Theoretical and STS works at Princeton University was supported by the Gordon and Betty Moore Foundation (GBMF4547; M.Z.H.).
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STM experiments were performed by N.S., M.S.H., Y.-X.J. and M.L. in consultation with J.-X.Y. and M.Z.H. Crystal growth was carried out by Z.W., Y.L., Y.Yang, Z.Y. and S.J. Transmission electron microscopy measurements were performed by G.C. and N.Y. Theoretical calculations regarding the higher-order band topology were mainly carried out by C.Y. under the supervision of F.Z., in consultation with M.S.H., J.X.Y., Y.C.L., T.R.C., T.N., Y.Yao and M.Z.H. Figure development and writing of the paper were undertaken by N.S., M.S.H., J.-X.Y., F.Z. and M.Z.H. M.Z.H. supervised the project. All the authors discussed the results, interpretation and conclusion.
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Extended data
Extended Data Fig. 1 Intra-unit cell modulation of differential conductance.
a, Topography image of a clean region. b, Corresponding dI/dV map taken at V = 600 mV. c, Intensity plot of the dI/dV spectrum taken along the line in a.
Extended Data Fig. 2 Bias dependence of the monolayer edge state.
a, Topographic image of an monolayer step edge. b, corresponding dI/dV maps, taken at V = 0 mV, -75mV, and -600mV.
Extended Data Fig. 3 Anisotropic in-plane magnetic field response of the edge state.
a, Field dependent differential spectra taken on the edge and away from the edge, denoted with red and blue curves, respectively. Spectra are offset for clarity. b, Topography and the corresponding field dependent dI/dV maps (shown by using the same color scale) further elucidating the anisotropic in-plane magnetic field response of the edge state.
Extended Data Fig. 4 High-resolution imaging of the monolayer step edge.
We show the height profile across a monolayer step edge (marked on lower inset image), in comparison with that from a surface far from step edge (mark on the upper inset image).
Extended Data Fig. 5 Tunnelling spectroscopy for both edges of a monolayer step.
a, Topographic image of right and left monolayer step edges (AB type). b, Differential spectra taken at the left AB monolayer step edge (red), at the right AB monolayer step edge (violet), and away from the edges (blue) reveal the presence of gapless edge states in both AB edges. The inset shows the schematic of the monolayer step edge states.
Extended Data Fig. 6 Hinge state candidate for a four-layer step edge.
a. Topographic image and corresponding height profile of a four-layer step edge. b, Schematic of a four-layer edge showing quantum hybridization of the quantum spin Hall edge states for neighboring layers. The destructive hybridization is illustrated by the lighter color of the edge states (red spheres). c, Differential spectra taken at the step edge (red) and away from the edge (blue) providing evidence for a candidate gapless hinge state.
Extended Data Fig. 7 Spectroscopy of the monolayer edge state at room temperature.
Differential spectra of the edge (red curves) and surface (dark and light blue curves), taken along the a-axis direction (marked on the corresponding topographic image in the right panel with a white line), exhibit an insulating gap away from edge and gapless edge state at T = 300 K. Spectra are offset for clarity, and their real-space locations are marked on the topography with color-coded dots. Dashed horizontal lines indicate zero density of states of the corresponding spectra.
Extended Data Fig. 8 Calculated helical edge state at a one-layer step edge.
a, The edge-projected band structure for a (001) monolayer ribbon on the top surface of Bi4Br4. The cyan bands are from the bulk and (001) surfaces of the system. The red bands are the helical edge states. Due to the inversion symmetry of the monolayer, the bands are doubly degenerate at each kb. The ribbon is infinitely long in the b direction and 200-chain wide in the a direction. b, The DOS plotted in a log scale corresponding to the band structure in a.
Extended Data Fig. 9 Calculated bilayer and twenty-layer step-edge states.
a, The edge-projected band structure for a (001) twenty-layer ribbon on the top surface of Bi4Br4. The cyan bands are from the bulk and (001) surfaces of the system. The orange bands are from the (100) and (-100) side surfaces of the ribbon. The red bands are the gapless hinge states. Due to the inversion asymmetry of even-layer systems, the bands are singly degenerate at each kb. The ribbon is infinitely long in the b direction and 50-chain wide in the a direction. b, The same as a but for a bilayer ribbon. The two helical edge states from the two monolayers are gapped at one side (orange) but remain almost gapless at the other side (red). c, The real space schematics of the surface and hinge/edge states in a and b.
Extended Data Fig. 10 Topologically protected boundary states in a nanorod geometry with inversion symmetry and C2 rotation symmetry around the [010] axis.
a, The nanorod of Bi4Br4 featuring helical hinge states from higher-order band topology and two surface Dirac cones on the (010) surface protected by the C2 rotation symmetry. b, Two possible inversion symmetric paths for the helical hinge states when the C2 symmetry is broken on the (010) surface.
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Shumiya, N., Hossain, M.S., Yin, JX. et al. Evidence of a room-temperature quantum spin Hall edge state in a higher-order topological insulator. Nat. Mater. 21, 1111–1115 (2022). https://doi.org/10.1038/s41563-022-01304-3
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DOI: https://doi.org/10.1038/s41563-022-01304-3
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