Classification of Crystalline Topological Insulators and Superconductors with Point Group Symmetries - INSPIRE

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Classification of Crystalline Topological Insulators and Superconductors with Point Group Symmetries

Nov 5, 2018

22 pages

Published in:

Phys.Rev.B 99 (2019) 7, 075105

Published: Feb 5, 2019

e-Print:

1811.01977 [cond-mat.mes-hall]

DOI:

10.1103/PhysRevB.99.075105 (publication)

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Abstract: (APS)

Crystalline topological phases have recently attracted a lot of experimental and theoretical attention. Key advances include the complete elementary band representation analyses of crystalline matter by symmetry indicators and the discovery of higher-order hinge and corner states. However, current classification schemes of such phases are either implicit or limited in scope. We present a scheme for the explicit classification of crystalline topological insulators and superconductors. These phases are protected by crystallographic point group symmetries and are characterized by bulk topological invariants. The classification paradigm generalizes the Clifford algebra extension process of each Altland-Zirnbauer symmetry class and utilizes algebras which incorporate the point group symmetry. Explicit results for all point group symmetries of three-dimensional crystals are presented as well as for all symmorphic layer groups of two-dimensional crystals. We discuss future extensions for treatment of magnetic crystals and defected or higher-dimensional systems as well as weak and fragile invariants.

Note:

25 pages, 15 figures, 16 tables

Electronic structure and strongly correlated systems

References(117)

Figures(31)

[1]

Topological Insulators

M.Z. Hasan
(
- Princeton U.
)
,
C.L. Kane
(
- Pennsylvania U.
)

- Rev.Mod.Phys. 82 (2010) 3045
•
e-Print:
- 1002.3895
•
DOI:
- 10.1103/RevModPhys.82.3045

[2]

Topological insulators and superconductors

Xiao Liang Qi
(
- UC, Santa Barbara and
- Stanford U.
)
,
Shou Cheng Zhang
(
- Stanford U.
)

- Rev.Mod.Phys. 83 (2011) 4, 1057-1110
•
e-Print:
- 1008.2026
•
DOI:
- 10.1103/RevModPhys.83.1057

[3]

Classification of topological quantum matter with symmetries

- Rev.Mod.Phys. 88 (2016) 3, 035005
•
e-Print:
- 1505.03535
•
DOI:
- 10.1103/RevModPhys.88.035005

[4]

Weyl and Dirac Semimetals in Three Dimensional Solids

N.P. Armitage
(
- Johns Hopkins U.
)
,
E.J. Mele
(
- Pennsylvania U.
)
,
Ashvin Vishwanath
(
- UC, Berkeley and
- Harvard U.
)

- Rev.Mod.Phys. 90 (2018) 1, 015001
•
e-Print:
- 1705.01111
•
DOI:
- 10.1103/RevModPhys.90.015001

[5]

Quantized Hall Conductance in a Two-Dimensional Periodic Potential

D.J. Thouless
(
- Washington U., Seattle
)
,
M. Kohmoto
(
- Washington U., Seattle
)
,
M.P. Nightingale
(
- Washington U., Seattle
)
,
M. den Nijs
(
- Washington U., Seattle
)

- Phys.Rev.Lett. 49 (1982) 405-408
•
DOI:
- 10.1103/PhysRevLett.49.405

[6]

Homotopy and Quantization in Condensed Matter Physics

J.E. Avron
(
- Liverpool U., Dept. Math. and
- Caltech
)
,
R. Seiler
(
- Brussels U.
)
,
B. Simon
(
- Liverpool U., Dept. Math. and
- Caltech
)

- Phys.Rev.Lett. 51 (1983) 51-53
•
DOI:
- 10.1103/PhysRevLett.51.51

[7]

Z-2 Topological Order and the Quantum Spin Hall Effect

C.L. Kane
(
- Pennsylvania U.
)
,
E.J. Mele
(
- Pennsylvania U.
)

- Phys.Rev.Lett. 95 (2005) 146802
•
e-Print:
- cond-mat/0506581
•
DOI:
- 10.1103/PhysRevLett.95.146802

[8]

Topological Superconductivity and Superfluidity

- Phys.Rev.Lett. 102 (2009) 18, 187001
•
e-Print:
- 0803.3614
•
DOI:
- 10.1103/PhysRevLett.102.187001

[9]

Classification of topological insulators and superconductors in three spatial dimensions

Andreas Schnyder
(
- Santa Barbara, KITP
)
,
Shinsei Ryu
(
- Santa Barbara, KITP
)
,
Akira Furusaki
(
- Wako, RIKEN
)
,
Andreas Ludwig
(
- UC, Santa Barbara
)

- Phys.Rev.B 78 (2008) 19, 195125
•
e-Print:
- 0803.2786
•
DOI:
- 10.1103/PhysRevB.78.195125

[10]

Quantum Spin Hall Effect in Graphene

C.L. Kane
(
- Pennsylvania U.
)
,
E.J. Mele
(
- Pennsylvania U.
)

- Phys.Rev.Lett. 95 (2005) 22, 226801
•
e-Print:
- cond-mat/0411737
•
DOI:
- 10.1103/PhysRevLett.95.226801

[11]

Quantum Spin Hall Insulator State in HgTe Quantum Wells

et al.

- Science 318 (2007) 5851, 1148047
•
DOI:
- 10.1126/science.1148047

[12]

Topological Insulators in Three Dimensions

- Phys.Rev.Lett. 98 (2007) 10, 106803
•
e-Print:
- cond-mat/0607699
•
DOI:
- 10.1103/PhysRevLett.98.106803

[13]

Topological invariants of time-reversal-invariant band structures

- Phys.Rev.B 75 (2007) 12, 121306
•
e-Print:
- cond-mat/0607314
•
DOI:
- 10.1103/PhysRevB.75.121306

[14]

R. Roy

- Phys.Rev.B 79 (2009) 195322
•
DOI:
- 10.1103/PhysRevB.79.195322

[15]

Unpaired Majorana fermions in quantum wires

Alexei Kitaev
(
- Microsoft, Redmond and
- Landau Inst.
)

- Phys.Usp. 44 (2001) 10S, 131-136
•
e-Print:
- cond-mat/0010440
•
DOI:
- 10.1070/1063-7869/44/10S/S29

[16]

Paired states of fermions in two-dimensions with breaking of parity and time reversal symmetries, and the fractional quantum Hall effect

N. Read
(
- Yale U.
)
,
Dmitry Green
(
- Yale U.
)

- Phys.Rev.B 61 (2000) 10267
•
e-Print:
- cond-mat/9906453
•
DOI:
- 10.1103/PhysRevB.61.10267

[17]

R.S.K. Mong
,
A.M. Essin
,
J.E. Moore

- Phys.Rev.B 81 (2010) 245209
•
DOI:
- 10.1103/PhysRevB.81.245209

[18]

L. Fu

- Phys.Rev.Lett. 106 (2011) 106802
•
DOI:
- 10.1103/PhysRevLett.106.106802

[19]

R.-J. Slager
,
A. Mesaros
,
V. Juriči
,
J. Zaanen

- Nature Phys. 9 (2013) 98
•
DOI:
- 10.1038/nphys2513

[20]

Classification of topological insulators and superconductors in the presence of reflection symmetry

- Phys.Rev.B 88 (2013) 7, 075142
•
e-Print:
- 1303.1843
•
DOI:
- 10.1103/PhysRevB.88.075142

[21]

W.A. Benalcazar
,
J.C.Y. Teo
,
T.L. Hughes

- Phys.Rev.B 89 (2014) 224503
•
DOI:
- 10.1103/PhysRevB.89.224503

[22]

Bulk Invariants and Topological Response in Insulators and Superconductors with Nonsymmorphic Symmetries

- Phys.Rev.B 92 (2015) 19, 195116
•
e-Print:
- 1507.00984
•
DOI:
- 10.1103/PhysRevB.92.195116

[23]

K. Shiozaki
,
M. Sato
,
K. Gomi

- Phys.Rev.B 91 (2015) 155120
•
DOI:
- 10.1103/PhysRevB.91.155120

[24]

Topological Phases Protected By Reflection Symmetry and Cross-cap States

Gil Young Cho
(
- Illinois U., Urbana
)
,
Chang-Tse Hsieh
(
- Illinois U., Urbana
)
,
Takahiro Morimoto
(
- Wako, RIKEN
)
,
Shinsei Ryu
(
- Illinois U., Urbana
)

- Phys.Rev.B 91 (2015) 195142
•
e-Print:
- 1501.07285
•
DOI:
- 10.1103/PhysRevB.91.195142

[25]

B.-J. Yang
,
T. Morimoto
,
A. Furusaki

- Phys.Rev.B 92 (2015) 165120
•
DOI:
- 10.1103/PhysRevB.92.165120

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