Geometrical and Algebraic Aspects of Condensed Matter Physics

凝聚态物理的几何和代数方面

• 批准号: 15540364
• 负责人: HATSUGAI Yasuhiro
• 金额: $ 2.24万
• 依托单位: the University of Tokyo
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2003
• 资助国家: 日本
• 起止时间: 2003 至 2004
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-15540364/
• 关键词: Topological Order; Anisotropic Superconductivity; Carbon 2D systems; Edge States; Quantum Liquids; Topological Invariants; Quantum Hall Effects; Quantum Entanglements; 幾何学的位相; カーボンナノチューブ; 局所磁気秩序; 時間反転対称性の破れ; ベリー接続; 非可換チャーン数; カーボン; 量子力学; 相分

It has been recognized that some of physically important quantum states are not well characterized by conventional order parameters. In such cases, geometrical phases which are characteristic in quantum physics play an important role. We try to characterize the states by the word "topological orders". Some of such states are polyacetylenes, quantum Hall states, two dimensional Carbon sheets, anisotropic superconductors with time reversal symmetry breaking and so on. In most cases, the topological orders are hidden in the bulk and reveal their characters near boundaries or defects as generalized edge states. Some of low dimensional quantum liquids can be also in the classes where topological invariants based on the Berry's connection may replace the conventional order parameters.

人们已经认识到，一些物理上重要的量子态不能很好地用常规的序参量来表征。在这种情况下，量子物理学中特有的几何相位起着重要的作用。我们试图用“拓扑序”这个词来描述这些状态。这类态包括聚乙炔、量子霍尔态、二维碳片、时间反演对称性破缺的各向异性超导体等，在大多数情况下，拓扑序隐藏在体材料中，在边界或缺陷附近表现为广义边缘态。某些低维量子液体也可以是基于Berry连接的拓扑不变量可以取代常规序参数的一类。

项目成果

Characterization of Topological insulator

拓扑绝缘体的表征

• 发表时间: 2005
• 期刊: J. Phy. Soc. Jpn. (Lett.) 74
• 作者: H.Taniguchi;Y.Morita;Y.Hatsugai;Y.Hatsugai
• 通讯作者: Y.Hatsugai

Zero energy edge states and chiral symmetry breaking at edges of graphite sheets

石墨片边缘的零能边缘态和手性对称性破缺

• 发表时间: 2004
• 期刊: Physica E 22
• 作者: S.Ryu;Y.Hatsugai
• 通讯作者: Y.Hatsugai

S.Ryu, Y.Hatsugai: "Zero energy edge states and chiral symmetry brealing at edges of graphite sheet"Physica E. (出版予定). (2004)

S.Ryu，Y.Hatsugai：“石墨片边缘的零能量边缘态和手性对称性破坏”Physica E.（即将出版）。

Quasiparticle structure in the vicinity of the Heisenberg model in one and higher dimensions

一维及更高维度海森堡模型附近的准粒子结构

• 发表时间: 2004
• 期刊: Phys. Rev. B 70
• 作者: Y.Morita;Y.Hatsugai;Y.Otsuka
• 通讯作者: Y.Otsuka

Y.Morita, S.Ryu, Y.Hatsugai: "Recent research develompmet in Physics, 4 "Emergence off(2+1)-dim. Dirac Fermion in condensed Matter""Transworld Reserch Network, India. 463-483(20) (2003)

Y.Morita、S.Ryu、Y.Hatsugai：“物理学的最新研究进展，4”Emergence off(2 1)-dim。