The classification of topological insulators and superconductors for non-spatial and spatial symmetries
Chiu, Ching-Kai
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https://hdl.handle.net/2142/44335
Description
Title
The classification of topological insulators and superconductors for non-spatial and spatial symmetries
Author(s)
Chiu, Ching-Kai
Issue Date
2013-05-24T22:08:12Z
Director of Research (if dissertation) or Advisor (if thesis)
Stone, Michael
Doctoral Committee Chair(s)
Ryu, Shinsei
Committee Member(s)
Stone, Michael
Chiang, Tai-Chang
Gilbert, Matthew J.
Cooper, S. Lance
Department of Study
Physics
Discipline
Physics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
classification
topological insulators
topological superconductors
topological crystalline insulators
Abstract
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.
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