Symmetry-enforced two-dimensional Dirac node-line semimetals

doi: 10.1088/2752-5724/aca816

1.
Department of Physics and Beijing Key Laboratory of Opto-electronic Functional Materials & Micro-nano Devices, Renmin University of China, Beijing 100872, People’s Republic of China
2.
Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences, Beijing 100190, People’s Republic of China

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Corresponding author: E-mail: liuzxphys@ruc.edu.cn; E-mail: kliu@ruc.edu.cn; E-mail: zlu@ruc.edu.cn

摘要

Abstract: Based on symmetry analysis and lattice model calculations, we demonstrate that Dirac nodal line (DNL) can stably exist in two-dimensional (2D) nonmagnetic as well as antiferromagnetic systems. We focus on the situations where the DNLs are enforced by certain symmetries and the degeneracies on the DNLs are inevitable even if spin-orbit coupling is strong. After thorough analysis, we find that five space groups, namely 51, 54, 55, 57 and 127, can enforce the DNLs in 2D nonmagnetic semimetals, and four type-III magnetic space groups (51.293, 54.341, 55.355, 57.380) plus eight type-IV magnetic space groups (51.299, 51.300, 51.302, 54.348, 55.360, 55.361, 57.387 and 127.396) can enforce the DNLs in 2D antiferromagnetic semimetals. By breaking these symmetries, the different 2D topological phases can be obtained. Furthermore, by the first-principles electronic structure calculations, we predict that monolayer YB₄C₄ is a good material platform for studying the exotic properties of 2D symmetry-enforced Dirac node-line semimetals.
- symmetry-enforced /
- Dirac nodal line semimetals /
- nonsymmorphic space group /
- antiferromagnetic systems
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Figure 1. (a) The BZ of square lattice. Nonsymmorphic symmetry protects the Dirac line without (b) and with (c). The red dots represent high-symmetry points. The NSOC represents no spin-orbital coupling.

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Figure 2. (a) The square lattice with p4/mbm space group symmetry. The black and blue lines indicate the nearest hopping t and second nearest hopping t₂. The spin-orbital coupling term $i λ$ , for one spin flavor, is shown by the red arrows. (b) The band structure of lattice model with parameter $λ = t_{2} = t$ along the high-symmetry directions. Lattice model and band structures: (c)-(d) breaking $T$ and $I$ with an out-of plane antiferromagnetic order indicated by the green arrow; (e)-(f) breaking $I$ symmetry with the chemical potential $\pm μ$ according to the green/red sites and the spin-orbital coupling term $i λ_{2}$ indicated by the purple arrows.

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Figure 3. (a) and (b) are the crystal structure of YB₄C₄ viewed along [001] and [100] directions, respectively. The red, blue and green balls represent Y, B and C atoms. (c) Phonon spectrum of monolayer YB₄C₄ along the high-symmetry directions.

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Figure 4. The electronic band structures of monolayer YB₄C₄ along the high-symmetry direction (a) without and (b) with SOC. The both +’ and -’ represent eigenvalue of M_z. (c) The three-dimensional electronic band structure. The NSOC represents no spin-orbital coupling.

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