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

classification;topological insulators;topological superconductors;topological crystalline insulators

Chiu, Ching-Kai

关键词: classification;    topological insulators;    topological superconductors;    topological crystalline insulators;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/44335/Ching-Kai_Chiu.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

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.