奈米圖樣化的二維電子系統中拓樸絕緣體物理之研究

Abstract

我們用理論探索在奈米圖模下二維電子氣可能實現的人造拓樸絕緣體。二維電子氣的高遷移率與成熟的製程技術吸引對於拓樸絕緣體上較完計畫標題:研究在奈米圖模下二維電子氣的拓樸絕緣體物理 1. 去探索奈米圖模下二維電子氣具有的拓樸絕緣體物理 2. 對以後的研究建立一個在二維電子氣的製程科技可實現的新穎機能基礎理論框架 整尺度物理研究的可能性。我們特別關注的是自旋軌道交互作用,包含本質自旋軌道交互作用,像在奈米圖模下二維電子氣的Rahsba, Dresselhaus自旋軌道交互作用。這些效應造成的能隙打開和邊緣態將被研究。 奈米圖模下二維電子氣包括中空圓,奈米閘極和磁通量晶格之各種形式晶格將被研究。自旋軌道交互作用可由均勻或週期的閘極圖模所造成。探討拓樸絕緣體對晶格具有和不具有反轉對稱的相關性質。中空圓使用硬牆式位能而鬆餅形位能可使用奈米閘極控制。研究在高對稱點K,M,Γ上由於自旋軌道交互作用引起的能階交叉和能隙打開,以及其他在布里淵區內的k點。布洛赫函數可用晶格中心的圓柱形波函數構成,將之推廣到二維磁通量晶格由於自旋軌道交互作用引起的能隙打開,對於每個佔據能帶可以計算Berry曲率和Chern數。透過直接計算邊緣態的波函數以及色散關係可以引入適當的邊界條件。我們特別想探討樣品邊緣方向性對於邊緣態的相關性。 我們的目標是對以後研究建立一個在二維電子氣可實現的新穎機能理論框架。

Title of the proposal: A study on the topological insulator physics in nano-patterned 2DEG The goals in this study are 1. to explore the topological insulator physics in nano-patterned 2DEG, 2. to establish a basic theoretical framework for later study on novel functionalities made possible by the 2DEG fabrication technologies. We propose to explore theoretically the possibility of realizing artificial topological insulator (TI) in nano-patterned two-dimensional electron-gas (2DEG). The high mobility of the 2DEG and the associated sophisticated fabrication technologies already established for 2DEG make this possibility attractive for a fuller scale study on the TI physics. Particular attention will go to the effects of spin-orbit interactions (SOI), including intrinsic SOIs such as the Rashba-type and Dresselhaus-type SOIs, on the nano-patterned 2DEG. Their effects on gap opening and edge states will be studied. Nano-patterned 2DEG includes void lattices, nano-gate lattices and magnetic flux lattices. The SOIs considered are either uniform or periodic, in direct correspondence to the gate pattern. Lattices with inversion and without inversion symmetry will be studied to explore its connection to the robustness of the TI effects. Various types of lattices will be studied. Hard wall potential model will be used for the void and muffin-tin potential model will be used for the nano-gate. Features of energy level crossing or gap opening will be studied at the high symmetry points, such as the K, M, and theΓpoints, and at other k points in the Brillouin zone. Detail analysis of the Bloch wavefunction in terms of the cylindrical wavefunctions centered at a lattice site will be carried out and the insights will be applied to the study of magnetic flux lattices in 2DEG. Gap opening due to SOI, the effects on the corresponding Berry curvature and the Chern number for each such occupied band will be calculated. Appropriate boundary conditions will be introduced for a direct calculation of the edge state dispersions and edge state wavefunction. In particular, the dependence of the edge states on the orientation of the edges will be explored. In all, we aim at establishing a theoretical framework for later study on novel functionalities made possible by the 2DEG.