Unconventional line defects engineering in two-dimensional boron monolayers

Shao-Gang Xu, Chang-Chun He, Yu-Jun Zhao, Hu Xu, and Xiao-Bao Yang

Phys. Rev. Materials 5, 044003 – Published 29 April 2021

Abstract

Line defects (LDs) are a kind of lattice imperfection widely existing in two-dimensional materials, which may play a significant role in the properties of materials. Different from the negative effect of LDs for stability in most 2D materials, we have proposed a simple universal rule to construct stable 2D boron isomers based on the LDs engineering, where the self-assembled monolayers are unconventionally enhanced. Based on the self-assembly of LDs from $β_{12}$ and $χ_{3}$ monolayers, we have found several boron monolayers with higher stability on the Ag (111) substrate than the experimental phases, and two monolayers in our prediction have been confirmed by the recent experiments. Notably, the mechanical response of the boron monolayers also can be enhanced by the LDs, indicating the potential application for advanced flexible electronic devices.

Received 20 January 2021
Accepted 16 April 2021

DOI:https://doi.org/10.1103/PhysRevMaterials.5.044003

Physics Subject Headings (PhySH)

Polycrystals Structural properties

2-dimensional systems

First-principles calculations High-throughput calculations

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Shao-Gang Xu ¹, Chang-Chun He², Yu-Jun Zhao², Hu Xu^1,*, and Xiao-Bao Yang ^2,†

¹Department of Physics, Guangdong Provincial Key Laboratory of Computational Science and Material Design, Guangdong-Hong Kong-Macao Joint Laboratory for Photonic-Thermal-Electrical Energy Materials and Devices, Southern University of Science and Technology, Shenzhen 518055, People's Republic of China
²Department of Physics, South China University of Technology, Guangzhou 510640, People's Republic of China

^*xuh@sustech.edu.cn
^†scxbyang@scut.edu.cn

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Issue

Vol. 5, Iss. 4 — April 2021

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Images

Figure 1
(a) Top view of the typical LDs in graphene, $h$ -BN, and ${MoS}_{2}$ . (b) The relative formation energy of the LDs, where the corresponding pristine phases were set to zero point.
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Figure 2
(a) The sketch map of the formation of $β_{2 - 2}$ monolayer based on the α ribbons self-assembly. (b) The similar formation mechanism of $β_{3 - 3}$ monolayer. (c) The schematic diagram of constructing any $β_{n_{1} - n_{2} - ... - n_{N}}$ monolayer based on the α ribbons self-assembly. (d) represents a long-range order candidate of $β_{2 - 3}$ monolayer. The black dashed lines in (a), (b) mark the unit cell of the monolayer.
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Figure 3
(a) The average formation energies $E_{form}$ of boron monolayers as a function of the vacancy density υ, and the three kinds of hollow dots represent three type combinations. (b) The average formation energies $E_{form}$ as a function of the AEC parameter λ. The α monolayer is set as the reference phase in (a), (b), which is set to zero. (c) The formation mechanism of $β_{3 - 3 - 3 - 4}$ monolayer based on the α ribbons self-assembly.
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Figure 4
(a) PDOS of the five boron monolayers. The green lines show the ( $p_{x} + p_{y}$ ) states, and the orange lines represent the out-of-plane $p_{z}$ states. Arrows mark the dip in the $p_{z}$ states near the $E_{F}$ . (b) The COHP plots for the four boron monolayers. (c) Bonding analysis for the $β_{3 - 3 - 3 - 4}$ monolayer. The left part shows the charge difference, and the right part shows the possible 2c–2e and 3c–2e bond distributions. The percentages of the color bar are signed with the peak amplitude value for the isosurface located at the left side, and the occupation numbers (ON) of the 2c–2e and 3c–2e bonds are listed on the right side.
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Figure 5
(a) Configurational energy spectra of the $δ_{A - n * B}$ boron monolayers, and the formation mechanism of $δ_{A - B}$ monolayer. (b) The formation mechanism of $δ_{A - 4 B}$ monolayer; the right part represents the top view of the $δ_{A - 4 B}$ monolayer on the Ag (111) substrates and the corresponding simulated STM image. (c) The average formation energy of the boron monolayers on the Ag (111) substrates; the bars highlighted with dashed lines represent the current experimental phases. (d) Calculated Young's modulus for the typical 2D materials and several boron monolayers; $x$ and $y$ correspond to the armchair and zigzag directions for the honeycomb lattice. (e) Calculated orientation-dependent Young's modulus Y(θ) in N/m and Poisson's ratio P(θ) for the two boron monolayers.
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