Topology of crystalline insulators and superconductors

By Ken Shiozaki, Masatoshi Sato. 2014

362 citations recorded by the source corpus.

We complete a classification of topological phases and their topological defects in crystalline insulators and superconductors. We consider topological phases and defects described by noninteracting Bloch and Bogoliubov–de Gennes Hamiltonians that support additional order-two spatial symmetry, besides any of 10 classes of symmetries defined by time-reversal symmetry and particle-hole symmetry. The additional order-two spatial symmetry we consider is general and it includes Z 2 global symmetry, mirror reflection, twofold rotation, inversion, and their magnetic point group symmetries. We find that the topological periodic table shows a periodicity in the number of flipped coordinates under the order-two spatial symmetry, in addition to the Bott periodicity in the space dimensions. Various symmetry-protected topological phases and gapless modes will be identified and discussed in a unified framework. We also present topological classification of symmetry-protected Fermi points. The bulk classification and the surface Fermi point classification provide a realization of the bulk-boundary correspondence in terms of the K theory.

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

View Paper: https://www.semanticscholar.org/paper/e219b04b4cd5637f57d55094f672517a5e0c51e9

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. Masatoshi Sato
2. K. Kawabata
3. Y. Ando
4. Ken Shiozaki
5. Masahito Ueda
6. Luka Trifunovic
7. P. Brouwer
8. Tanmoy Das

In Condensed Matter Physics

1. Masahito Ueda
2. Y. Ando
3. Luka Trifunovic
4. P. Brouwer
5. K. Kawabata
6. Masatoshi Sato
7. Ken Shiozaki
8. Yuto Ashida

Citations in the corpus

• Topological superconductors: a review (2016, background): “Using the K-theory, one can show that the possible topological number for H(k, r) depends only on δ = d − D.”
• Topological Phases of Non-Hermitian Systems (2018, methodology): “Our guiding principles also enable a systematic application of the K theory [118], a technique widely used in classifying Hermitian topological systems [44,46,51], to the non-Hermitian AZ classes, leading to a complete classification in all spatial dimensions.”
• Symmetry and Topology in Non-Hermitian Physics (2018, methodology): “Our strategy is to reduce this non-Hermitian problem to the established topological classification of Hermitian Hamiltonians in the AZ symmetry class without [206–208] and with [213] additional symmetries.”
• 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)”