论文标题
拓扑带系统和有限尺寸效果
Topological Band Systems and Finite Size Effects
论文作者
论文摘要
关于拓扑绝缘体的最新发现一直在促进理论和实验研究。在本论文中，审查了拓扑绝缘子和量子厅效应的基本概念，将讨论重点放在边缘状态及其频段结构上。描述了带有刺穿磁性的晶格模型，并为有和没有现场障碍的有限系统提出了Hofstadter模型。给出了具有合成维度的光学晶格中基于冷原子的实验过程的概述。为了理解这些冷原子的这些小型系统模仿拓扑绝缘子的行为，对某些有限尺寸效应进行了分析，并使用扰动理论提出了频带结构中的间隙开口。
The recent discoveries about topological insulators have been promoting theoretical and experimental research. In this dissertation, the basic concepts of topological insulators and the Quantum Hall Effect are reviewed focusing the discussion on edge states and their band structure. Lattice models with pierced magnetism are described and the Hofstadter model is presented for bounded systems with and without an in-site disorder. An overview of the experimental procedure based on cold atoms in optical lattices with synthetic dimensions is given. In order to understand to what extent these small systems of cold atoms mimic the behaviour of a topological insulator, an analysis of some finite size effects is provided and a deduction of the gap opening in the band structure is presented using perturbation theory.
