雙層SnTe 拓樸晶體絕緣體中的激子凝聚

Abstract

在本篇論⽂中，討論了在雙層SnTe 拓樸晶體絕緣體材料中的激⼦凝聚現象。SnTe 是⼀個拓樸晶體絕緣體，意即這個材料中的拓墣性質是來⾃於晶體的對稱性，⽽在SnTe 中，引發拓樸性質的對稱性為晶格的鏡像對稱性。因為拓樸性質來⾃於晶格的對稱性，SnTe 表⾯態的性質會和晶格⾯的⽅向有關。在所有表⾯態中，⼜以 (001) ⽅向的表⾯態最為有趣，因為他的能帶是由兩個Dirac cones 所組成，並且我們能在這個邊界態的價帶和導帶看到特殊的雙錐形結構和奇特的⾃旋組態。在我們的系統中，利⽤了雙層SnTe (001) 的表⾯態來形成激⼦凝聚，當有⼀外加電場通⼊我們的系統，正負電荷會被極化到不同的層中，透過電荷間相互的庫倫交互作⽤⼒，正負電荷便會形成激⼦。由於我們利⽤平均場的⽅法來處理系統中的庫倫交互作⽤⼒，所以這個雙層系統的哈密頓量必須⽤⾃洽的⽅法來解出能量最低的狀態。數值的結果顯⽰在我們的系統中得確有激⼦凝聚的現象產⽣。處此之外，因為SnTe (001)表⾯態特殊的⾃旋結構，在我們的雙層系統中，⾃旋提供了我們額外的資訊去確定激⼦凝聚在這個系統中存在的可能性。

In this thesis, we consider the exciton condensation in bilayer SnTe topological crystalline insulator in which the topological characters are protected by mirror symmetry. Due to the lattice symmetries in SnTe, the surface gapless states have different characteristics in different crystal orientations. Among all possible gapless states in SnTe, the (001) surface state is the most interesting one whose dispersion is formed by the overlapping of two Dirac cones. This special dispersion reveals a peculiar two-cone structure and exotic spin textures in the conduction and the valence bands. Our bilayer system is composed of two SnTe (001) surface states which sandwich a separation layer. By applying an external electric field, the charges with opposite sign are separated into the different layers. The Coulomb interaction between these charges would couple them to form excitons. The Hamiltonian of our bilayer system needs to be solved self-consistently due to the mean-field formalism of the Coulomb interaction. The numerical result shows the existence of the exciton condensates. Especially, according to the non-trivial spin textures of the SnTe (001) surface state, the spin textures of the bilayer system can provide us additional information to detect and confirm the exciton condensation phase.