自旋軌道作用對奈米圖形二維電子系統的影響

Effects spin-orbit interaction on a nano-patterned two-dimensional electron gas

蘇韋綾

指導教授 ： 朱仲夏

國立交通大學/理學院/電子物理系所/碩士(2011年)

https://doi.org/10.6842/NCTU.2011.00589

摘要

我們考慮電子狀態在三角形週期電壓下的二維電子氣體中，有多對狄拉克角錐結
構在倒空間中的K 點被找到。由於週期性的平面電位差造成的有效自旋軌道交互作用，導致在狄拉克點上的錐狀結構打開一個能隙。
與石墨石烯的Chern 值做比較,此週期性三角結構系統的Chern 值不為零，是由於此系統(三角形週期晶格)有以垂直平面方向做轉軸旋轉60 度倍數的系統對稱性。
由於拓撲學中的不變量Z2 值以及Chern 值，可預期在樣品邊界擁有相反方向傳輸的邊緣態以及量子自旋霍爾效應是存在此系統的。此自旋軌道交互作用是造成此系統有拓撲絕緣相位的原因。

關鍵字

自旋軌道 ； HASH(0xb881b68) ； 二維電子氣體

並列摘要

We consider the electronic state of a two-dimensional electron gas in a muffin-tin potential triangular lattice. Several Dirac cone structures at the K points in the reciprocal space have been obtained.
Effects of spin-orbit interaction due to the in-plane potential gradient of the mu±n-tin potential have been studied in detail. We find that gap opening at the Dirac points can lead to global gaps. In contrast to the graphene case, the Chern number of an energy band for a given spin state is nonzero. This is due to the rotational symmetry by rotating about an axis normal to the system by 60 degree.
As a result the system has a topological Z2 invariant and we expected it to support helical edge states in the open boundary case. The spin-orbit interaction is thus shown to drive the system into a topological insulating phase.

並列關鍵字

spin-orbit ； HASH(0xb881cd0) ； two-dimentional electron gas

參考文獻

[1] Tight-Binding Based Modelling of Graphene Antidot Structures,Rene Petersen.

[2] Topics in advanced quantum mechanics, Barry R. Holstein (Addison Wesley).

[3] H.-A. Engel, B. I. Halperin, and E. I. Rashba, Phys. Rev.Lett.95, 166605 (2005).

[4] Spin-Orbit Coupling in Two-Dimensional Electron and Hole systems, Roland Winkler

(Springer, 2003).