一般注記The topological classi cation of condensed matter is a central topic in the last decade. Using the concept, the gapped electric states have been classi ed into the different topological phases.At present, the topological classi cation is based on the spatial dimension of materials and by the invariance of the electric states under the fundamental symmetries: time-reversal, particlehole, chiral, and the mirror symmetries. The electric states belonging to each topological phase have the common topological properties such as the quantized Hall conductivity in the class A insulators in two-dimension. In particular, the interface gapless states at the boundary of two topological phases is a key feature commonly in topological materials, which has been understood in terms of a conjecture so-called bulk-boundary correspondence. In three-spatial-dimension, the original classi cation predicts no topologically nontrivial phase in the absence of the fundamental symmetries. However, a number of interface gapless states appear even in the absence of fundamental symmetries. Therefore, to understand topological states appearing in realistic materials, more detailed classi cation is necessary in addition to the original one.In this paper, we show topologically nontrivial states in three-dimension without any fundamental symmetries and propose a novel classi cation to characterize such topological electric states. In our classi cation, the topological numbers are de ned in lower dimensionalpartial Brillouin zones speci ed by xed wavenumbers. For instance, we characterize the three-dimensional topological electric states by using the Chern number de ned in the two-dimensional partial Brillouin zone. It is known that topological states characterized by theChern number are robust under the various symmetry-breaking perturbations. Owing to this property, we successfully explain the transition or the crossover from the topological insulator to the topological semimetal under the strong Zeeman elds. We also discuss that the topological number in the partial Brrilouin zone well topologically distinguishes two topological materials classi ed into the same topological phase in the original classi cation.
(主査) 准教授 浅野 泰寛, 教授 矢久保 考介, 教授 丹田 聡, 准教授 鈴浦 秀勝
工学院（応用物理学専攻）
コレクション（個別）国立国会図書館デジタルコレクション > デジタル化資料 > 博士論文
受理日（W3CDTF）2015-02-03T05:25:05+09:00
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