Emergence of Topologically Nontrivial Spin-Polarized States in a Segmented Linear Chain

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Emergence of Topologically Nontrivial Spin-Polarized States in a Segmented Linear Chain

Thang Pham, Sehoon Oh, Scott Stonemeyer, Brian Shevitski, Jeffrey D. Cain, Chengyu Song, Peter Ercius, Marvin L. Cohen, and Alex Zettl

Phys. Rev. Lett. 124, 206403 – Published 20 May 2020

See Viewpoint: Topological States in a Segmented Chain

Abstract

The synthesis of new materials with novel or useful properties is one of the most important drivers in the fields of condensed matter physics and materials science. Discoveries of this kind are especially significant when they point to promising future basic research and applications. van der Waals bonded materials comprised of lower-dimensional building blocks have been shown to exhibit emergent properties when isolated in an atomically thin form [1–8]. Here, we report the discovery of a transition metal chalcogenide in a heretofore unknown segmented linear chain form, where basic building blocks each consisting of two hafnium atoms and nine tellurium atoms ( ${Hf}_{2} {Te}_{9}$ ) are van der Waals bonded end to end. First-principle calculations based on density functional theory reveal striking crystal-symmetry-related features in the electronic structure of the segmented chain, including giant spin splitting and nontrivial topological phases of selected energy band states. Atomic-resolution scanning transmission electron microscopy reveals single segmented ${Hf}_{2} {Te}_{9}$ chains isolated within the hollow cores of carbon nanotubes, with a structure consistent with theoretical predictions. van der Waals bonded segmented linear chain transition metal chalcogenide materials could open up new opportunities in low-dimensional, gate-tunable, magnetic, and topological crystalline systems.

Received 25 January 2020
Accepted 26 March 2020

DOI:https://doi.org/10.1103/PhysRevLett.124.206403

Physics Subject Headings (PhySH)

Edge states Electronic structure of atoms & molecules First-principles calculations Rashba coupling Topological materials

0-dimensional systems Quantum wires

Density functional theory Scanning transmission electron microscopy Z_2 symmetry

Condensed Matter, Materials & Applied Physics

Viewpoint

Topological States in a Segmented Chain

Published 20 May 2020

A segmented chain of molecules held together by van der Waals forces may host spin-polarized, topologically protected electron states.

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Authors & Affiliations

Thang Pham^1,2,3,4,*, Sehoon Oh ^1,2,*, Scott Stonemeyer^1,2,4,5, Brian Shevitski^1,2, Jeffrey D. Cain ^1,2,4, Chengyu Song ⁶, Peter Ercius ⁶, Marvin L. Cohen^1,2, and Alex Zettl^1,2,4,†

¹Department of Physics, University of California at Berkeley, Berkeley, California 94720, USA
²Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
³Department of Materials Science and Engineering, University of California at Berkeley, Berkeley, California 94720, USA
⁴Kavli Energy NanoSciences Institute at the University of California at Berkeley, Berkeley, California 94720, USA
⁵Department of Chemistry, University of California at Berkeley, Berkeley, California 94720, USA
⁶National Center for Electron Microscopy, The Molecular Foundry, One Cyclotron Road, Berkeley, California 94720, USA

^*These authors contributed equally to this work.
^†To whom all correspondence should be addressed. azettl@berkeley.edu

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Issue

Vol. 124, Iss. 20 — 22 May 2020

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Images

Figure 1
The linear segmented chain of ${Hf}_{2} {Te}_{9}$ . (a) Aberration-corrected HAADF STEM image of a segmented chain of ${Hf}_{2} {Te}_{9}$ encapsulated within a double-walled CNT. A false color [Fire in the Look up Table (LUT) of ImageJ] is applied to visually aid the analysis. The structure consists of regularly spaced segments of ${Hf}_{2} {Te}_{9}$ (or ${Te}_{3} − Hf − {Te}_{3} − Hf − {Te}_{3}$ ). (b),(c) Atomic structure of the linear segmented chain of ${Hf}_{2} {Te}_{9}$ obtained from DFT calculations. (b) The obtained atomic structure of the segmented chain inside an (8,8) single-wall CNT is shown, where Hf and Te atoms are represented as red and blue spheres, respectively, and the chain direction is set to the $z$ direction. (c) The building block of a ${Hf}_{2} {Te}_{9}$ unit is shown without a CNT for clearer presentation of the atomic structure, in which the mirror planes perpendicular to $y$ and $z$ axes are represented by white dashed lines and denoted as $M_{y}$ and $M_{z}$ , respectively. (d) Multislice simulated STEM image of a segment using the proposed atomic structure. (e) A composite STEM image generated from averaging experimentally collected 227 orientationally similar single segments (average cell).
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Figure 2
Calculated electronic structures of the single-atomic segmented chain of ${Hf}_{2} {Te}_{9}$ . (a)–(c) The electronic structure of an isolated segmented chain of ${Hf}_{2} {Te}_{9}$ . The band structures obtained (a) without and (b) with considering SOI, and (c) PDOS obtained with SOI. (d)–(f) The electronic structure of the segmented chain ${Hf}_{2} {Te}_{9}$ near the chemical potential. The band structures obtained (d) without and (e) with considering SOI, and (f) PDOS obtained with SOI. (d),(e) The color of the band lines represents the expectation value of the $y$ component of OAM $⟨ L_{y} ⟩$ [in (d)] and spin $⟨ S_{y} ⟩$ [in (e)]. In (a)–(f), the chemical potential is set to zero and marked with a horizontal dashed line.
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Figure 3
Calculated atomic and electronic structures of a linear segmented chain of ${Hf}_{2} {Te}_{9}$ encapsulated in an (8,8) CNT. (a),(b) Atomic structure of a segmented chain of ${Hf}_{2} {Te}_{9}$ encapsulated within a CNT in (a) side view and (b) axial view, where Hf, Te, and C atoms are represented as red, blue, and white spheres, respectively. (c),(d) Electronic structure of the segmented chain ${Hf}_{2} {Te}_{9}$ encapsulated in the CNT. (c) Band structure and (d) PDOS obtained with SOI. In (c),(d), the Fermi energy is set to zero and marked with a horizontal dashed line. In (c), band structures represented by red and blue dots are projected onto spin up and spin down, respectively, in the $y$ direction of the segmented chain and unfolded with respect to the first Brillouin zone of the unit cell of the segmented chain, while the bands represented by black dots are projected onto the CNT and unfolded with respect to the first Brillouin zone of the unit cell of the CNT. The center of the Brillouin ( $k = 0$ ) is denoted by $Γ$ , while $Z_{Hf 2 Te 9}$ and $Z_{CNT}$ denote the zone boundaries for the segmented chain and the CNT, respectively.
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Figure 4
Topological properties of a single-atomic segmented chain of ${Hf}_{2} {Te}_{9}$ with various chemical potentials. (a),(b) The atomic and electronic structures of the segmented chain of ${Hf}_{2} {Te}_{9}$ without a chemical potential change are shown for comparison. The highest occupied band is nontrivial. (c),(d) The atomic and electronic structure of the segmented chain of ${Hf}_{2} {Te}_{9}$ with $2 e / f . u .$ subtracted in the DFT calculations. In (a),(c), Hf and Te atoms are represented as red and blue spheres, respectively. In (c), the subtracted charge is schematically represented by yellow spheres. In (b),(d), the energy level of the top of the highest occupied band is set to zero for easy comparison, and the chemical potential is represented by green dashed lines. Two time-reversal channels of the highest occupied bands, $s = I$ and II, are represented by blue and red lines, respectively. The symmetry-protected topological invariance $Z_{2}$ is 0 for a neutral system and 1 for the $h$ -doped system.
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