Metal-insulator transition in quasi-one-dimensional ${\mathrm{HfTe}}_{3}$ in the few-chain limit

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Metal-insulator transition in quasi-one-dimensional ${HfTe}_{3}$ in the few-chain limit

Scott Meyer, Thang Pham, Sehoon Oh, Peter Ercius, Christian Kisielowski, Marvin L. Cohen, and Alex Zettl

Phys. Rev. B 100, 041403(R) – Published 9 July 2019

Abstract

The quasi-one-dimensional linear chain compound ${HfTe}_{3}$ is experimentally and theoretically explored in the few- to single-chain limit. Confining the material within the hollow core of carbon nanotubes allows isolation of the chains and prevents the rapid oxidation which plagues even bulk ${HfTe}_{3}$ . High-resolution transmission electron microscopy combined with density functional theory calculations reveals that, once the triple-chain limit is reached, the normally parallel chains spiral about each other, and simultaneously a short-wavelength trigonal antiprismatic rocking distortion occurs that opens a significant energy gap. This results in a size-driven metal-insulator transition.

Received 1 March 2019
Revised 7 June 2019

DOI:https://doi.org/10.1103/PhysRevB.100.041403

Physics Subject Headings (PhySH)

Encapsulation Metal-insulator transition

Crystal growth Density functional theory Scanning transmission electron microscopy Transmission electron microscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Scott Meyer^1,2,3,4,*, Thang Pham^1,3,4,5,*, Sehoon Oh^1,4, Peter Ercius⁶, Christian Kisielowski⁶, Marvin L. Cohen^1,4, and Alex Zettl^1,3,4,†

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

^*These authors contributed equally to this work.
^†Corresponding author: azettl@berkeley.edu

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Vol. 100, Iss. 4 — 15 July 2019

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Images

Figure 1
Crystal view along the (a) $b$ axis and (b) $c$ axis, highlighting the quasi-one-dimensional nature of the trigonal prismatic ${HfTe}_{3}$ chains, with the unit cell boxed in black. Hf and Te atoms are represented by red and green spheres, respectively.
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Figure 2
Encapsulation series from many- to single-chain limit of ${HfTe}_{3}$ . High-resolution transmission electron microscopy images of (a) many-, (b) triple-, (c) double-, and (d) single-chain limits of ${HfTe}_{3}$ encapsulated within a carbon nanotube. A simplified cross-sectional representation of the filled carbon nanotube is shown to the right of each image, with a model of the chains’ filling behavior shown below each image. Scale bars measure 2 nm. All images are underfocused, where Hf and Te atoms appear dark.
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Figure 3
Encapsulation of single, double, and triple ${HfTe}_{3}$ chains. Scanning transmission electron microscopy image of (a) triple, (b) double, and (c) single ${HfTe}_{3}$ chains encapsulated within a carbon nanotube. Hf and Te atoms appear white in the images. Atomic models below (b) and (c) demonstrate the orientation of the chain(s), where Hf and Te atoms are red and green, respectively. The node-to-node length of the spiraling in (a) and (b) is marked by white dashed lines. Scale bars measure 1 nm.
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Figure 4
Calculated atomic and electronic structures of single-chain ${HfTe}_{3}$ . The atomic and electronic structures of single-chain HfTe3 isolated in vacuum with (a)–(e) TP and (f)–(j) TAP geometry, and (k)–(n) the TAP single-chain encapsulated inside a (8,8) CNT are presented. In the atomic structure, the red and green spheres represent Hf and Te atoms, respectively. The basic units of (c) the TP and (h) TAP geometry are shown for comparison. In the band structures, the chemical potential is set to zero and marked with a horizontal dashed line. In (m), the bands represented by red and gray lines are projected onto the single-chain ${HfTe}_{3}$ and CNT, respectively, and unfolded with respect to the first Brillouin zone of the unit cell of the single chain with periodicity $λ = b_{0}$ and the CNT, where zone boundaries for the chain and CNT are denoted as $Z_{HfT e_{3}}$ and $Z_{CNT}$ , respectively.
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Figure 5
Calculated atomic and electronic structures of spiraling double- and triple-chain ${HfTe}_{3}$ . The atomic and electronic structures of spiral (a)–(c) double and (d)–(f) triple chains of ${HfTe}_{3}$ isolated in vacuum are presented. In the axial view along the $b$ axis of the unit cell, the red and green spheres represent Hf and Te atoms, respectively. In (b), (e) the band structures, the chemical potential is set to zero and marked with a horizontal dashed line and unfolded with respect to the first Brillouin zone of the unit cell of the single chain with periodicity $λ = b_{0}$ , where the Brillouin zone center and the edge are denoted as Γ and $Z$ , respectively. The individual chains comprising triple and double chains rock into TAP geometry.
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Physical Review B

covering condensed matter and materials physics

Metal-insulator transition in quasi-one-dimensional ${HfTe}_{3}$ in the few-chain limit

Scott Meyer, Thang Pham, Sehoon Oh, Peter Ercius, Christian Kisielowski, Marvin L. Cohen, and Alex Zettl

Phys. Rev. B 100, 041403(R) – Published 9 July 2019

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Physical Review B

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Metal-insulator transition in quasi-one-dimensional HfTe3 in the few-chain limit

Scott Meyer, Thang Pham, Sehoon Oh, Peter Ercius, Christian Kisielowski, Marvin L. Cohen, and Alex Zettl

Phys. Rev. B 100, 041403(R) – Published 9 July 2019

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Metal-insulator transition in quasi-one-dimensional ${HfTe}_{3}$ in the few-chain limit