- 1'College of Mechanics, Changchun Institute of Technology, Changchun, China
- 2Engineering and Technology Center, The Fourth Medical College of Harbin Medical University, Harbin, China
- 3School of Chemistry, Harbin Normal University, Harbin, China
With the development of computer technology and theoretical chemistry, the speed and accuracy of first-principles calculations have significantly improved. Using first-principles calculations to predict new topological materials is a hot research topic in theoretical and computational chemistry. In this work, we focus on a well-known material, sodium chloride (NaCl), and propose that the triple point (TP), quadratic contact triple point (QCTP), linear and quadratic nodal lines can be found in the phonon dispersion of NaCl with Fm
Introduction
The recent rapid development in topological materials (Kong and Cui, 2011; Cava et al., 2013; Banik et al., 2018; Kumar et al., 2020; Li and Wei, 2021) makes chemists expect these materials to solve the current challenges in quantum chemistry. A series of topological materials, including topological insulators (Müchler et al., 2012; Bradlyn et al., 2017; Kou et al., 2017; Martín Pendás et al., 2019; Isaeva and Ruck, 2020), spin-gapless semiconductors (Gao et al., 2016; Wang et al., 2016; Wang, 2017; Sun et al., 2020; Yue et al., 2020), and topological semimetals/metals (Zhou et al., 2018a; Schoop et al., 2018; Xu et al., 2020a; Klemenz et al., 2020; Zhao et al., 2020), were predicted by researchers, and some of them are confirmed in experiments. Among them, topological semimetals/metals (Zhong et al., 2016; Zhang et al., 2018; Jin et al., 2019a; Jin et al., 2019b; He et al., 2019; Wang et al., 2020a; Wang et al., 2020b; Xu et al., 2020b; Guo et al., 2020; Jin et al., 2021) always have nontrivial band crossings in their electronic band structures. In addition to their potential applications in technology, they also provide a platform for the study of basic quasiparticles in low cost experiments.
Recently, parallel to electrons, topological concepts have been extended to boson systems such as phonons in crystal materials, classical elastic waves in macroscopic artificial phonon crystals, and magnetic oscillators in magnets. Especially important is that the topological phonon in crystal materials (Jin et al., 2018; Liu et al., 2019; Zheng et al., 2019; Liu et al., 2020; Xie et al., 2021) can provide a potential prospect for regulating heat transfer and electron-phonon interaction. It should be emphasized that the phonon is not limited by the principle of Pauli incompatibility, which means that the experimental detection can be carried out in the whole frequency region of the phonon spectrum.
This work will focus on a famous realistic material, sodium chloride (NaCl). NaCl is with the Fm
Methods
The crystal structure of Fm
Calculated Phonon Dispersion and the Related Topological Signatures
In Figure 2, we plotted the three-dimensional BZ and some high symmetry points, X, K, W, Y, L, and
FIGURE 2. Three-dimensional Brillouin zone (BZ) and the two-dimensional (001) surface BZ. The X, K, W, Y, L, Γ are the symmetry points of 3D BZ. Γ, X, and X points are projected to
Moreover, from Figure 3, one obtains the following information: 1) Along the
One may wonder whether the doubly degenerate band along the
FIGURE 4. (A), (C) some selected symmetry points along the X-
A summary of this section is shown as follow: NaCl phonon hosts a QCTP at the
Calculated Surface States on (001) Surface BZ
In this section, we come to study the project surface states of the [001] NaCl phonons. As shown in Figure 2, we selected some symmetry points,
For clarity, we also exhibit the iso-frequency surface contours at 4.86 THz and 4.57 THz in Figure 6A,B, respectively. In Figure 6A, the positions of the projected TP and the connected surface states are marked by a green dot and black arrows, respectively. In Figure 6B, the positions of the projected QCTP and the connected surface states are marked by a black dot and black arrows, respectively. The projected TP/QCTP connected surface states are visible.
Summary
In this study, we proposed the topological signatures of the NaCl’s phonon dispersion. A systematic theoretical investigation found that this material hosts quadratic and linear nodal lines, TP and QCTP in its phonon dispersion. The QCTP is located at the Γ position, the TP is along the X-
Data Availability Statement
The original contributions presented in the study are included in the article/Supplementary Material, further inquiries can be directed to the corresponding authors.
Author Contributions
LZ, and FF: conceptualization, methodology, software, formal analysis, data curation, and writing. KW, LC, HL, and LZ: investigation, funding, and project administration. All authors contributed to the article and approved the submitted version.
Funding
This work is supported by Topic Foundation of Changchun Institute of Technology (Grant No. 320200040), Young People Foundation of Changchun Institute of Technology (Grant No. 320200033), Doctor Foundation of Changchun Institute of Technology 2021, Natural Science Foundation of Heilongjiang Province (Grant No. LH 2020H067), Heilongjiang Postdoctoral Program (LBH-Q16173), Science and Technology Program of Academy of Medical Sciences of Heilongjiang Province (Grant No. 201805), Research Foundation of Education Bureau of Jilin Province (Grant No. JJKH20210666KJ).
Conflict of Interest
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
Publisher’s Note
All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.
Footnotes
1https://materialsproject.org/materials/mp-22862/
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Keywords: DFT, first-principles calculations, phonon dispersion, surface state, NaCl
Citation: Zhang L, Fang F, Cheng L, Lin H and Wang K (2021) Obvious Surface States Connecting to the Projected Triple Points in NaCl’s Phonon Dispersion. Front. Chem. 9:789522. doi: 10.3389/fchem.2021.789522
Received: 05 October 2021; Accepted: 18 October 2021;
Published: 15 November 2021.
Edited by:
Junjie He, Charles University, CzechiaReviewed by:
Zhimin Wu, Chongqing Normal University, ChinaMinquan Kuang, Southwest University, China
Copyright © 2021 Zhang, Fang, Cheng, Lin and Wang. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
*Correspondence: Kai Wang, wangkai@hrbmu.edu.cn; Li Zhang, lizhang@ccit.edu.cn
†These authors have contributed equally to this work