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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 |
This item appears in the following Collection(s)
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Dissertations and Theses - Physics
Dissertations in Physics -
Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois