Room-Temperature Topological Phase Transition in Quasi-One-Dimensional Material ${\mathrm{B}\mathrm{i}}_{\mathrm{4}}{\mathrm{I}}_{\mathrm{4}}$

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Room-Temperature Topological Phase Transition in Quasi-One-Dimensional Material ${B i}_{4} I_{4}$

Jianwei Huang, Sheng Li, Chiho Yoon, Ji Seop Oh, Han Wu, Xiaoyuan Liu, Nikhil Dhale, Yan-Feng Zhou, Yucheng Guo, Yichen Zhang, Makoto Hashimoto, Donghui Lu, Jonathan Denlinger, Xiqu Wang, Chun Ning Lau, Robert J. Birgeneau, Fan Zhang, Bing Lv, and Ming Yi

Phys. Rev. X 11, 031042 – Published 24 August 2021

Abstract

Quasi-one-dimensional (1D) materials provide a superior platform for characterizing and tuning topological phases for two reasons: (i) existence for multiple cleavable surfaces that enables better experimental identification of topological classification and (ii) stronger response to perturbations such as strain for tuning topological phases compared to higher dimensional crystal structures. In this paper, we present experimental evidence for a room-temperature topological phase transition in the quasi-1D material ${Bi}_{4} I_{4}$ , mediated via a first-order structural transition between two distinct stacking orders of the weakly coupled chains. Using high-resolution angle-resolved photoemission spectroscopy on the two natural cleavable surfaces, we identify the high-temperature $β$ phase to be the first weak topological insulator with two gapless Dirac cones on the (100) surface and no Dirac crossing on the (001) surface, while in the low-temperature $α$ phase, the topological surface state on the (100) surface opens a gap, consistent with a recent theoretical prediction of a higher-order topological insulator beyond the scope of the established topological materials databases that hosts gapless hinge states. Our results not only identify a rare topological phase transition between first-order and second-order topological insulators but also establish a novel quasi-1D material platform for exploring unprecedented physics.

Received 7 February 2021
Revised 30 April 2021
Accepted 27 May 2021

DOI:https://doi.org/10.1103/PhysRevX.11.031042

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Topological materials Topological phase transition

Angle-resolved photoemission spectroscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Jianwei Huang ^1,*, Sheng Li^2,*, Chiho Yoon ^2,3,*, Ji Seop Oh ^4,1, Han Wu¹, Xiaoyuan Liu², Nikhil Dhale², Yan-Feng Zhou², Yucheng Guo ¹, Yichen Zhang¹, Makoto Hashimoto⁵, Donghui Lu⁵, Jonathan Denlinger⁶, Xiqu Wang⁷, Chun Ning Lau⁸, Robert J. Birgeneau ^4,9,†, Fan Zhang ^2,‡, Bing Lv^2,§, and Ming Yi ^1,∥

¹Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
²Department of Physics, The University of Texas at Dallas, Richardson, Texas 75080-3021, USA
³Department of Physics and Astronomy, Seoul National University, Seoul 08826, Korea
⁴Department of Physics, University of California, Berkeley, California 94720, USA
⁵Stanford Synchrotron Radiation Lightsource, SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA
⁶Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
⁷Department of Chemistry, University of Houston, Houston, Texas 77204, USA
⁸Department of Physics, The Ohio State University, Columbus, Ohio 43210, USA
⁹Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA

^*These authors contributed equally to this work.
^†robertjb@berkeley.edu
^‡zhang@utdallas.edu
^§blv@utdallas.edu
^∥mingyi@rice.edu

Popular Summary

A topological insulator (TI) is a fascinating state of matter in which its interior is insulating whereas its exterior conducts robustly. “Strong TIs,” in which every surface is conductive, are abundant in nature. However, “weak TIs,” in which only selective surfaces are conductive, as well as “higher-order TIs,” in which the robust conduction channels are confined to selected hinges, remain elusive. Both the weak and higher-order TIs host helical edge states—the electronic highway of spins and the cornerstone of topological electronics. Here, we provide the first unambiguous experimental evidence of a weak TI in a quasi-1D crystal of ${B i}_{4} I_{4}$ .

In a weak TI crystal, the outer edges of the atomic layers support a topological surface state. This surface is special, because there is now electrical conduction that behaves like a two-way highway around each layer. The conduction along the two ways can only cross talk between adjacent layers. This translates into a pair of so-called “gapless Dirac cones,” a key observational signature of weak TIs wherein the electronic band structure looks like two separate but connected light cones. In our experiments, we find evidence of this signature in ${B i}_{4} I_{4}$ . By lowering the temperature, the topological side surface states also develop compelling evidence for a phase transition into a higher-order TI.

Our work not only establishes a versatile quasi-1D topological material platform but also paves the way for a room-temperature topological switch that can control the dimensions of topological conduction.

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Vol. 11, Iss. 3 — July - September 2021

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Condensed Matter Physics

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Figure 1
Crystal structure and sample characterization. (a) Temperature-dependent resistivity data for both cooling and warming curves. The inset is the enlarged view showing the hysteresis behavior of the first-order transition. (b) Images of a ${Bi}_{4} I_{4}$ crystal showing the cleavable (001) and (100) surfaces where the grid is 1 mm. (c),(f) The real-space crystal structure and the reciprocal space lattice from the $h 0 l$ layer precession images integrated from x-ray diffraction data for the $α − {Bi}_{4} I_{4}$ phase. The shaded region is the structural unit cell. (d),(g) The unit cell volume and refined lattice parameter $a$ from x-ray diffraction reflecting the $α$ to $β$ structural transition. (e),(h) Same as (c),(f) but for the $β − {Bi}_{4} I_{4}$ phase. (i),(j) The bulk and projected surface Brillouin zones (BZ) of $α − {Bi}_{4} I_{4}$ and $β − {Bi}_{4} I_{4}$ .
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Figure 2
Electronic structure from different surfaces. (a) Fermi surface mapping of $α − {Bi}_{4} I_{4}$ on the $(100)^{'}$ surface, with the surface BZ marked by gray rectangles (the solid one corresponds to $α − {Bi}_{4} I_{4}$ and the dashed one to $β − {Bi}_{4} I_{4}$ ). (b) Constant energy contour of $α − {Bi}_{4} I_{4}$ on the (001) surface. (e)–(h) Measured band dispersions of $α − {Bi}_{4} I_{4}$ along the cut 1 to cut 4 indicated in (a) and (b). Related surface states (SS) and bulk states (BS) are marked by arrows. (c),(d) and (i)–(l) Same as the top row but for $β − {Bi}_{4} I_{4}$ . All band images are divided by the Fermi-Dirac function. (m) Band image along the cut 5 except taken at $k_{y} = 0$ . Cut 5 was drawn intentionally off center to not block the Fermi surface image. The red dashed lines are sinusoidal fittings of the band image showing a periodicity of $0.3 Å^{- 1}$ due to band doubling, which corresponds to the $(100)^{'}$ surface. (n) Band image along the cut 6 indicated in (b). The black arrow shows a periodicity of $0.88 Å^{- 1}$ which corresponds to the (001) surface. (o) Measured dispersions in $α − {Bi}_{4} I_{4}$ along high symmetry cuts. (p) Calculated bulk band structure of $α − {Bi}_{4} I_{4}$ projected onto the (001) surface (see Supplemental Material [33]). (q),(r) Same as (o),(p) but for $β − {Bi}_{4} I_{4}$ . A clear doubling of the bulk valence bands is evident from $β − {Bi}_{4} I_{4}$ to $α − {Bi}_{4} I_{4}$ in both the measured and calculated dispersions. All measurement temperatures are as indicated.
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Figure 3
Bulk band doubling across the phase transition. (a)–(c) Warm-up and (d)–(f) cool-down band images measured along cut 1 indicated in Fig. 2 at selected temperatures. (g), (h) Corresponding MDCs at $- 1.2 eV$ during warm-up and cool-down, respectively. (i) Warm-up and (j) cool-down false-color images showing a more detailed temperature evolution of the MDCs indicated in (a). (k) Example of a MDC fitted by two Lorentzian peaks. (l) Full width at half maximum of the MDC fittings indicated in (k) as a function of temperature. The warm-up results are shifted 0.04 $Å^{- 1}$ upward. (m) The separation of the peak positions of the MDC fittings indicated in (k) as a function of temperature.
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Figure 4
Surface states evolution across the phase transition. (a) Band image along cut 4 on the (001) surface indicated in Fig. 2 of $α − {Bi}_{4} I_{4}$ as well as its corresponding EDC stacks. The red EDC corresponds to $k = 0$ . The green dots track the peak positions of the bulk band which reveal a gap opening of $\sim 85 meV$ . (b) Same as (a) but of $β − {Bi}_{4} I_{4}$ . A gap opens at $k = 0$ of $\sim 100 meV$ . (c) Band image along cut 1 on the $(100)^{'}$ surface indicated in Fig. 2 of $α − {Bi}_{4} I_{4}$ as well as its corresponding EDC stacks. The blue dots track the surface state which reveal a $\sim 35 meV$ gap opening. (d) Same as (c) but of $β − {Bi}_{4} I_{4}$ . A gapless Dirac surface state is observed. (e) 3D view of the electronic structure on the $(100)^{'}$ surface of $α − {Bi}_{4} I_{4}$ . A quasi-1D Dirac-like surface state is observed. (f) Same as (e) but of $β − {Bi}_{4} I_{4}$ . The quasi-1D Dirac surface state reveals the weak TI property. (g) Schematics (see Supplemental Material [33]) showing the higher-order TI state of $α − {Bi}_{4} I_{4}$ with a particular surface termination. Upper panel: all the bulk states and surface states are gapped, whereas a helical hinge state around the top surface exists in the surface state gap. Lower panel: the enlarged $(100)^{'}$ surface state features a band doubling and a small gap. (h) Schematics (see Supplemental Material [33]) showing the weak TI state of $β − {Bi}_{4} I_{4}$ . Upper panel: the bulk states and (001) surface state are gapped, whereas there is a quasi-1D gapless Dirac surface state on the (100) surface. Lower panel: the enlarged (100) surface state features two gapless Dirac cones.
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Physical Review X

Room-Temperature Topological Phase Transition in Quasi-One-Dimensional Material Bi4I4

Jianwei Huang, Sheng Li, Chiho Yoon, Ji Seop Oh, Han Wu, Xiaoyuan Liu, Nikhil Dhale, Yan-Feng Zhou, Yucheng Guo, Yichen Zhang, Makoto Hashimoto, Donghui Lu, Jonathan Denlinger, Xiqu Wang, Chun Ning Lau, Robert J. Birgeneau, Fan Zhang, Bing Lv, and Ming Yi

Phys. Rev. X 11, 031042 – Published 24 August 2021

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Room-Temperature Topological Phase Transition in Quasi-One-Dimensional Material ${B i}_{4} I_{4}$