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Title:The classification of topological insulators and superconductors for non-spatial and spatial symmetries
Author(s):Chiu, Ching-Kai
Director of Research:Stone, Michael
Doctoral Committee Chair(s):Ryu, Shinsei
Doctoral Committee Member(s):Stone, Michael; Chiang, Tai-Chang; Gilbert, Matthew J.; Cooper, S. Lance
Department / Program:Physics
Discipline:Physics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(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.
Issue Date:2013-05-24
URI:http://hdl.handle.net/2142/44335
Rights Information:Copyright 2013 Ching-Kai Chiu
Date Available in IDEALS:2013-05-24
Date Deposited:2013-05


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