The classification of topological insulators and superconductors for non-spatial and spatial symmetries

We study a topological classification of insulators and superconductors in the presence of non-spatial discrete symmetries in the Altland-Zirnbauer classification and spatial symmetries in any spatial dimension. We provide a unified method, the construction of bulk Dirac Hamiltonians in minimal matrix dimension, to classify topological phases. Using this method, we first reproduce the classification of non-spatial symmetric topological insulators and superconductors in the Altland-Zirnbauer symmetry classes. Such non-trivial topological insulators and superconductors possess protected gapless modes in each boundary. Furthermore, we extend the classification to spatial symmetric systems, such as reflection symmetry. When a specific boundary that does not break system's symmetries is introduced in these non-trivial topological systems, gapless modes are present at this boundary.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Physics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2013

Author dc:creator

• Chiu, Ching-Kai

Contributors dc:contributor

• Stone, Michael
• Ryu, Shinsei
• Chiang, Tai-Chang
• Gilbert, Matthew J.
• Cooper, S. Lance

• classification
• topological insulators
• topological superconductors
• topological crystalline insulators

Statement dc:rights

• Copyright 2013 Ching-Kai Chiu

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/44335

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/44335