利用第一原理理論計算尋找強軌道自旋耦合與拓樸絕緣材料

Abstract

近年來人們發現在某些薄膜材料所產生的表面態具有非常特殊的電子自旋排列，而這種特殊的電子自旋排列主要起因於自旋軌道角動量耦合效應。故人們開始紛紛投入具有強自旋軌道耦合效應的材料，並將它們製作成薄膜，試圖利用這種特殊的自旋關係來製作量子元件。然而在這種材料中最引起人們注意的即是具有非常特別之表面態的拓樸絕緣體。 我們試圖尋找一些人們預測因為強軌道自旋耦合效應所引起的拓樸絕緣體材料。我們分別計算了Bi2TeI、Bi4Se3以及Bi3Se4這三種材料的能帶結構，並且判斷這三種材料的薄膜是否有成為拓樸絕緣體的可能。但最後我們發現此三種材料都沒有機會變成拓樸絕緣體。 在本文的第二部分我們將利用第一原理態密度泛函理論去探討在Bi2Te2Se以及Bi2Se3之薄膜結構所造成的表面能帶，即俗稱的表面態。利用計算不同厚度的薄膜，來探討厚度對於這兩種材料的能帶結構影響。隨後我們把外加電場加在垂直於Bi2Se3薄膜平面的方向，於是發現了因為外加電場所造成的能帶分裂，即Rashba效應。我們計算了各種不同大小的外加電場所產生的能帶結構。由簡單的量子力學理論預測到了Rashba效應的大小應是與外加電場成正比，但我們發現Rashba效應的大小並不與外加電場成正比，而是與電場大小呈現震盪起伏的關係。

In recent years, people have found some surface states which featured the fantastic electric spin orientation. It is caused by strong spin-orbit coupling. Many people began to study the strong spin-orbital coupling material. They tried to make thin films of such materials to find some special states that can be the brand new quantum devices. Therefore, the most interesting of them are the topological insulators. There are two edge states which are protected by time reversal symmetry at the surface of a topological insulator. A lot of materials were predicted to be the topological insulators. In this thesis, we considered some possible topological insulators,Bi2TeI , Bi4Se3 and Bi3Se4. We calculated the band structures of them to determine whether they could be the topological insulators. Unfortunately, we did not find out any topological state. We also calculated the surface states of Bi2Te2 Se thin films and Bi2Se3 thin films. The band structures of thin films with different thickness were calculated to find how its electronic structure would depend on their thickness. After that we turn on the electric field that was perpendicular to the Bi2e3 thin films. We found the spin splitting on the band structure of Bi2Se3 thin films. We changed the magnitude of electric field, and found the variant magnitude of band splitting depends strongly on different electric field. According to the Rashba model, the Rashba parameter should be proportional to the magnitude of electric field. Surprisingly, by our computation results show that the Rashba parameter oscillated with the magnitude of electric field.