The space group classification of topological band-insulators

By Robert-Jan Slager, A. Mesaros, V. Juričić, J. Zaanen. Nature Physics, 2012

555 citations recorded by the source corpus.

Topological band-insulators (TBIs) are bulk insulating materials, which in the presence of time-reversal symmetry feature topologically protected metallic states on their surface or edge. They have recently been discovered in two- and three-dimensional materials with a strong spin–orbit coupling. These unusual states of quantum matter may host Majorana fermions and provide the condensed-matter realization of the exotic theta-vacuum. The existing classification of TBIs departs from time-reversal symmetry, but the role of the crystal-lattice symmetries in the physics of these topological states has remained elusive. Here we provide the classification of TBIs protected not only by time-reversal, but also by crystalline symmetries. We find three broad classes of topological states: Γ states robust against general time-reversal invariant perturbations; translationally active states protected from elastic scattering, but susceptible to topological crystalline disorder; valley topological insulators sensitive to the effects of non-topological and crystalline disorder. These three classes give rise to 18 different two-dimensional, and, at least 70 three-dimensional TBIs, opening up a route for the systematic search for new types of TBIs. Topological insulators are now shown to be protected not only by time-reversal symmetry, but also by crystal lattice symmetry. By accounting for the crystalline symmetries, additional topological insulators can be predicted.

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

View Paper: https://www.semanticscholar.org/paper/218339ed01f91479e8fad3d2eb6e2016e736daa0

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. K. Kawabata
2. Masatoshi Sato
3. Ashvin Vishwanath
4. Ken Shiozaki
5. E. Khalaf
6. Masahito Ueda
7. H. Po
8. Tanmoy Das

In Condensed Matter Physics

1. Masahito Ueda
2. K. Kawabata
3. Ken Shiozaki
4. Yuto Ashida
5. Z. Gong
6. Masatoshi Sato
7. E. Khalaf
8. H. Po

In Materials Chemistry

1. Ashvin Vishwanath
2. E. Khalaf
3. H. Po
4. Hsin Lin
5. Arun Bansil
6. Tanmoy Das
7. Masatoshi Sato
8. Ken Shiozaki

Citations in the corpus

• Symmetry and Topology in Non-Hermitian Physics (2018, background): “Since topology crucially depends on the underlying manifold, non-Hermiticity is expected to alter the topological classification of insulators and superconductors [206–219].”
• Experimental observation of non-Abelian topological acoustic semimetals and their phase transitions (2021, background): “[8] Robert-Jan Slager, Andrej Mesaros, Vladimir Juričić, and Jan Zaanen, “The space group”
• Topological Phases of Non-Hermitian Systems (2018, background): “[48] Robert-Jan Slager, Andrej Mesaros, Vladimir Juričić, and Jan Zaanen, “The space group classification of topological bandinsulators,” Nat.”
• Colloquium : Topological band theory (2016, background): “(Hasan and Kane 2010; Kitaev 2009; Schnyder et al. 2008; Fang, Gilbert, and Bernevig 2012; Slager et al. 2013; Chiu, Yao, and Ryu 2013; Hughes, Prodan, and Bernevig 2011; Shiozaki and Sato 2014)”