Topological nodal line semimetal in an orthorhombic graphene network structure

Jian-Tao Wang, Changfeng Chen, and Yoshiyuki Kawazoe

Phys. Rev. B 97, 245147 – Published 28 June 2018

Abstract

Topological semimetals are a fascinating class of quantum materials that possess extraordinary electronic and transport properties. These materials have attracted great interest in recent years for their fundamental significance and potential device applications. Currently a major focus in this research field is to theoretically explore and predict and experimentally verify and realize material systems that exhibit a rich variety of topological semimetallic behavior, which would allow a comprehensive characterization of the intriguing properties and a full understanding of the underlying mechanisms. In this paper, we report on ab initio calculations that identify a carbon allotrope with simple orthorhombic crystal structure in $P b c m$ ( $D_{2 h}^{11}$ ) symmetry. This carbon allotrope can be constructed by inserting zigzag carbon chains between the graphene layers in graphite or by a crystalline modification of a (3,3) carbon nanotube with a double cell reconstruction mechanism. Its dynamical stability has been confirmed by phonon and molecular dynamics simulations. Electronic band calculations indicate that it is a nodal-line semimetal comprising two nodal lines that go through the whole Brillouin zone in bulk and a projected surface flat band around the Fermi level. The present findings establish an additional topological semimetal system in the nanostructured carbon allotropes family and offer insights into its outstanding structural and electronic properties.

Received 9 February 2018
Revised 21 May 2018

DOI:https://doi.org/10.1103/PhysRevB.97.245147

Physics Subject Headings (PhySH)

Carbon-based materials Node-line semimetals

First-principles calculations

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Jian-Tao Wang^1,2,*, Changfeng Chen³, and Yoshiyuki Kawazoe^4,5

¹Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
²School of Physics, University of Chinese Academy of Sciences, Beijing 100049, China
³Department of Physics and High Pressure Science and Engineering Center, University of Nevada, Las Vegas, Nevada 89154, USA
⁴New Industry Creation Hatchery Center, Tohoku University, Sendai 980-8579, Japan
⁵Department of Physics and Nanotechnology, SRM Institute of Science and Technology, Kattankulathur 603203, Tamil Nadu, India

^*wjt@aphy.iphy.ac.cn

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Vol. 97, Iss. 24 — 15 June 2018

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Images

Figure 1
The crystal structure of so- $C_{12}$ in $P b c m$ ( $D_{2 h}^{11}$ ) symmetry. (a) The 12-atom unit cell of so- $C_{12}$ with lattice parameters $a = 4.313$ Å, $b = 8.604$ Å, and $c = 2.461$ Å, occupying the $4 d_{1}$ (0.0507, 0.2104, 0.25), $4 d_{2}$ (0.0763, 0.0351, 0.25), and $4 d_{3}$ (0.5783, 0.5052, 0.25) Wyckoff positions denoted by $C_{1}$ , $C_{2}$ , and $C_{3}$ , respectively. (b) A double cell reconstruction pathway from polymeric (3,3) CNT toward so- $C_{12}$ with bond breaking between atoms 6-7 and 16-17 at step 9 and between atoms 1-12 and 22-23 at step 13. The atoms are marked as red in tube I and black in tube II, respectively. The initial stage pathway from (3,3) CNT toward polymeric (3,3) CNT is shown in Fig. S1 in Supplemental Material [62]. (c) Enthalpy vs pathway from polymeric (3,3) CNT toward so- $C_{12}$ at 10 and 15 GPa.
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Figure 2
Calculated energy vs volume per atom for so- $C_{12}$ compared to graphite, diamond, fcc- $C_{60}$ [63], bco- $C_{16}$ [29], bct- $C_{4}$ [15], $M$ -carbon [14], bct- $C_{12}$ [28], ign- $C_{6}$ [27], and polymeric (3,3) CNT [61].
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Figure 3
Phonon band structures and partial density of states (PDOS) for so- $C_{12}$ . The peaks around 1443 and 1268 ${cm}^{- 1}$ are related to $s p^{2}$ and $s p^{3}$ bonding, respectively.
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Figure 4
Energy fluctuations of so- $C_{12}$ in AIMD simulations at 1200 and 1500 K. Insets depict the structural changes at step 1000 and 4000 during the simulations.
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Figure 5
Calculated bulk and surface band structures of so- $C_{12}$ at equilibrium lattice parameters. (a) The bulk band structure along several high-symmetry directions. $G_{1}$ and $G_{2}$ indicate the irreducible representations of the two crossing bands, respectively. (b) The Brillouin zone (BZ) with several high-symmetry momenta indicated, and the nodal lines (red), formed by the band crossing points, in the $G − Z − T − Y$ mirror plane. The $a$ and $b$ points represent the nodal point located along the $G − Z$ and $T − Y$ line, respectively. (c) The band-decomposed charge density isosurfaces ( $0.07 e / Å^{3}$ ) around the nodal point $b$ along the $T − Y$ direction in the BZ. (d,e) The (010) surface states obtained using a ten-layer-thick slab geometry along the [010] direction. The surface flat band (red line) can be inside or outside the surface projected nodal lines, depending on the termination of the surface without (d) or with (e) saturation by hydrogen atoms. The projected surface BZ $\bar{G} − \bar{Z} − \bar{T} − \bar{Y}$ is marked relative to $G − Z − T − Y$ in bulk in (b). (f) Partial charge density isosurfaces ( $0.05 e / Å^{3}$ ) related to the (red) surface bands in (d) at the $\bar{G}$ point. The outermost atoms are $C_{2}$ and $C_{3}$ with dangling bonds on $C_{2}$ sites.
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