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SCIENTIA SINICA Physica, Mechanica & Astronomica
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SCIENTIA SINICA Physica, Mechanica & Astronomica, Volume 50 , Issue 9 : 090002(2020) https://doi.org/10.1360/SSPMA-2020-0149

Research progress on topological nodal line semimetals

ZeYing ZHANG 1,2, BoTao FU 1,3, Zhi-Ming YU 1, YuGui YAO 1,*
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  • ReceivedApr 27, 2020
  • AcceptedJun 17, 2020
  • PublishedAug 11, 2020
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Abstract


Funded by

国家自然科学基金(11734003)

国家重点研发计划(2016YFA0300600)

中国科学院战略先导科技专项(B类)

中央高校基本科研业务费专项资金(ZY2018)


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    Figure 1

    (Color online) (a) Crystal structure of Cu2Si; (b) band structure when spin-orbit coupling is not considered; (c) Fermi surface of Cu2Si; (d) derivative constant energy contours measured using 30-eV p-polarized photons. Pictures are taken from ref. [58] with permission.

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    Figure 2

    (Color online) (a) Crystal structure of Ag2BiO3; (b) the band structure at the XURS plane. The eigenvalues of {Mx|01212} are shown.(c) The band structure of Ag2BiO3 along high symmetry line; (d) the Fermi surface of Ag2BiO3; (e) the calculated surface states of Ag2BiO3 on the (001) surface plane; (f) display of the gapless points in the extended Brillouin zone. The color represents the energy dispersion of each point with respect to the Fermi level. Pictures are taken from ref. [39] with permission.

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    Figure 3

    (Color online) (a) Crystal structure of XF3 (X=Pd, Mn); (b) band structure of PdF3, the red line stand for the first-principles calculation results, the black line is from the tight-binding mode. (c), (d) The profile of the gapless points of PdF3 in Brillouin zone, including the top views and the side views. Different colors correspond to different orientations of the nodal lines. (e) The surface states of PdF3 for surface (111). Pictures are taken from ref. [88] with permission.

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    Figure 4

    (Color online) (a) Schematic diagram of the D2d lattice model, including three C2 rotation axes and two mirror operations; (b) band structure with (the magnetization direction is parallel to the z-axis) and without spin-orbit coupling; (c), (d) the gapless point of the system in the Brillouin zone with respect to θ, where (c) is side view and (d) is top view. Pictures are taken from ref. [90] with permission.

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    Figure 5

    (Color online) (a)-(c) are the top view and side views of the crystal structure and the Brillouin zone of ZrPtGa, respectively; (d) calculated band structure along high symmetry lines for ZrPtGa with spin-orbit coupling; (e) the band dispersion around a generic point, where P and Q are the midpoints of Г-A and K-H, respectively. Pictures are taken from ref. [43] with permission.

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    Figure 6

    (Color online) (a) Schematic figure of a nodal loop, where q1 and q2 label the two mutually perpendicular transverse directions; (b) and (c) illustrate the type-I and type-II nodal loops dispersions along the q1 direction, respectively. Pictures are taken from ref. [42] with permission.

  • Table 1   All possible higher-order nodal line protected by crystalline symmetry. The zero-term in the effective Hamiltonian is omitted because it does not affect the classification of the nodal line. The form is taken from ref. [43]

    空间群号

    对应点群

    节线的阶

    k点路径

    不可约表示

    有效哈密顿量

    174

    C3h

    二次型

    Г-A

    {Г4, Г5}

    αq−2σ++H.c.

    187-190

    D3h

    二次型

    Г-A

    Г4

    αq−2σ++H.c.

    183-186

    C6v

    三次型

    Г-A

    Г9

    i (αq−3+βq−3)σ++H.c.