Symmetry guaranteed Dirac-line semimetals in two-dimensions against strong spin-orbit coupling

Guo, Deping; Guo, Peng‐Jie; Tan, Shiliang; Feng, Min; Cao, Limin; Liu, Zhengxin; Li, Kai; Lu, Zhong-Yi; Ji, Wei

doi:10.48550/arxiv.2012.15218

Cited by 4 publications

(8 citation statements)

References 8 publications

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“…Fourfold degenerate Dirac lines in 2D was recently proposed in Ref. [82,83]. It was shown that with SOC, the symmetries P , T , a screw axis S 2x and a vertical glide mirror G y can enforce a Dirac line on the k y = π path at the BZ boundary.…”

Section: D Nodal-line Tsmmentioning

confidence: 96%

“…Recently, trilayer Bi structure was also identified as a candidate to host such Dirac lines. [84,85] It was shown that with SOC, the symmetries P, T , a screw axis S 2x and a vertical glide mirror G y can enforce a Dirac line on the k y = π path at the BZ boundary. This Bi structure, called the brick phase tri-atomic layer Bi(110), was successfully grown on black phosphorous substrate in experiment.…”

Section: The 2d Nodal-line Tsmmentioning

confidence: 99%

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Two-dimensional topological semimetals*

Feng

Zhu

et al. 2021

Chinese Phys. B

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The field of two-dimensional topological semimetals, which emerged at the intersection of twodimensional materials and topological materials, have been rapidly developing in recent years. In this article, we briefly review the progress in this field. Our focus is on the basic concepts and notions, in order to convey a coherent overview of the field. Some material examples are discussed to illustrate the concepts. We discuss the outstanding problems in the field that need to be addressed in future research.

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Section: D Nodal-line Tsmmentioning

confidence: 96%

Section: The 2d Nodal-line Tsmmentioning

confidence: 99%

Two-dimensional topological semimetals*

Feng

Zhu

et al. 2021

Chinese Phys. B

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“…h∈H Tr W η 0 (h) 1. From the above expression of W η 0 (h), after some calculations (see appendix B) we obtain (42) Specially, if…”

Section: |H|mentioning

confidence: 97%

“…If the leading order of Γ(δk) is linear in δk, namely, Γ(δk) ∼ δk • Γ, then the dispersion around this high-degeneracy point forms a cone. For fermionic systems, a conic dispersion is called a Dirac cone [24][25][26][27][28][29][30][31][32][33] if d = 4 and if T = IT (I is the spacial inversion operation) is an element of G 0 (k) such that the energy bands are doubly degenerate away from k. On the other hand, if the degeneracy remains unchanged along a special line crossing the point k, then this line is called a nodal line [34][35][36][37][38][39][40][41][42][43][44].…”

Section: K • P Perturbation Around High Symmetry Pointsmentioning

confidence: 99%

A Hamiltonian approach for obtaining irreducible projective representations and the k ⋅ p perturbation for anti-unitary symmetry groups

Yang¹,

Yang²,

Fang³

et al. 2021

J. Phys. A: Math. Theor.

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As is known, the irreducible projective representations (Reps) of anti-unitary groups contain three different situations, namely, the real, the complex and quaternionic types with torsion number 1, 2, 4 respectively. This subtlety increases the complexity in obtaining irreducible projective Reps of anti-unitary groups. In the present work, a physical approach is introduced to derive the condition of irreducibility for projective Reps of anti-unitary groups. Then a practical procedure is provided to reduce an arbitrary projective Rep into direct sum of irreducible ones. The central idea is to construct a Hermitian Hamiltonian matrix which commutes with the representation of every group element g ∈ G, such that each of its eigenspaces forms an irreducible representation space of the group G. Thus the Rep is completely reduced in the eigenspaces of the Hamiltonian. This approach is applied in the k ⋅ p effective theory at the high symmetry points (HSPs) of the Brillouin zone for quasi-particle excitations in magnetic materials. After giving the criterion to judge the power of single-particle dispersion around an HSP, we then provide a systematic procedure to construct the k ⋅ p effective model.

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“…If the leading order of Γ(δk k k) is linear in δk k k, namely, Γ(δk k k) ∼ δk k k • Γ Γ Γ, then the dispersion around this highdegeneracy point froms a cone. For fermionic systems, a conic dispersion is called a Dirac cone [22][23][24][25][26][27][28][29][30][31] if d = 4 and if T = IT (I is the spacial inversion operation) is an element of G 0 (k k k) such that the energy bands are doubly degenerate away from k k k. On the other hand, if the degeneracy remains unchanged along a special line crossing the point k k k, then this line is called a nodal line [32][33][34][35][36][37][38][39][40][41][42].…”

Section: A K • P Perturbation Around High Symmetry Pointsmentioning

confidence: 99%

A Hamiltonian Approach for Obtaining Irreducible Projective Representations and the $k\cdot p$ Perturbation for Anti-unitary Symmetry Groups

Yang,

Fang

et al. 2021

Preprint

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As is known, the irreducible projective representations (Reps) of anti-unitary groups contain three different situations, namely, the real, the complex and quaternion types with torsion number 1,2,4 respectively. This subtlety increases the complexity in obtaining irreducible projective Reps of antiunitary groups. In the present work, a physical approach is introduced to derive the condition of irreducibility for projective Reps of anti-unitary groups. Then a practical procedure is provided to reduce an arbitrary projective Rep into direct sum of irreducible ones. The central idea is to construct a hermitian Hamiltonian matrix which commutes with the representation of every group element g ∈ G, such that each of its eigenspaces forms an irreducible representation space of the group G. Thus the Rep is completely reduced in the eigenspaces of the Hamiltonian. This approach is applied in the k • p effective theory at the high symmetry points (HSPs) of the Brillouin zone for quasi-particle excitations in magnetic materials. After giving the criterion to judge the power of single-particle dispersion around a HSP, we then provide a systematic procedure to construct the k • p effective model.

show abstract

Symmetry guaranteed Dirac-line semimetals in two-dimensions against strong spin-orbit coupling

Cited by 4 publications

References 8 publications

Two-dimensional topological semimetals*

Two-dimensional topological semimetals*

A Hamiltonian approach for obtaining irreducible projective representations and the k ⋅ p perturbation for anti-unitary symmetry groups

A Hamiltonian Approach for Obtaining Irreducible Projective Representations and the $k\cdot p$ Perturbation for Anti-unitary Symmetry Groups

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