Classification of reflection-symmetry-protected topological semimetals and nodal superconductors

By Ching-Kai Chiu, A. Schnyder. 2014

224 citations recorded by the source corpus.

While the topological classification of insulators, semimetals, and superconductors in terms of nonspatial symmetries is well understood, less is known about topological states protected by crystalline symmetries, such as mirror reflections and rotations. In this work, we systematically classify topological semimetals and nodal superconductors that are protected, not only by nonspatial (i.e., global) symmetries, but also by a crystal reflection symmetry. We find that the classification crucially depends on (i) the codimension of the Fermi surface (nodal line or point) of the semimetal (superconductor), (ii) whether the mirror symmetry commutes or anticommutes with the nonspatial symmetries, and (iii) how the Fermi surfaces (nodal lines or points) transform under the mirror reflection and nonspatial symmetries. The classification is derived by examining all possible symmetry-allowed mass terms that can be added to the Bloch or Bogoliubov--de Gennes Hamiltonian in a given symmetry class and by explicitly deriving topological invariants. We discuss several examples of reflection-symmetry-protected topological semimetals and nodal superconductors, including topological crystalline semimetals with mirror ${\mathbb{Z}}_{2}$ numbers and topological crystalline nodal superconductors with mirror winding numbers.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/7aa8c39222c33a21c31b7d7b67726f6f209d71d3

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. Ashvin Vishwanath
2. N. P. Armitage
3. E. Mele
4. Hsin Lin
5. Arun Bansil
6. M. Zahid Hasan
7. Su-Yang Xu
8. G. Bian

In Condensed Matter Physics

1. Ashvin Vishwanath
2. Su-Yang Xu
3. Ching-Kai Chiu
4. M. Zahid Hasan
5. Hsin Lin
6. G. Bian
7. N. P. Armitage
8. E. Mele

In Materials Chemistry

1. Ashvin Vishwanath
2. N. P. Armitage
3. E. Mele
4. Hsin Lin
5. Arun Bansil
6. M. Zahid Hasan
7. Su-Yang Xu
8. G. Bian

Citations in the corpus

• Weyl and Dirac semimetals in three-dimensional solids (2017, background): “The ten-fold symmetry classification of Hamiltonians based on their global time reversal, particle-hole and chiral symmetries can be extended to treat gapless systems protected by reflection symmetry (Chiu and Schnyder, 2014).”
• Drumhead Surface States and Topological Nodal-Line Fermions in TlTaSe2 (2015, background): “The topological nodal-line state in TlTaSe2 is in the class A+R (p = 2) of symmetryprotected semimetals [23, 25] and is conneted with spin-polarized “drumhead” surface modes.”