在陳絕緣體中由可變之磁化方向所引發的拓撲相變

Topological Phase Transitions in Chern Insulators with Tunable Magnetization Orientations

張睿安(Rui-An Chang)

指導教授 ： 張慶瑞

國立臺灣大學/理學院/應用物理研究所/碩士(2019年)

https://doi.org/10.6342/NTU201901054

摘要

一直以來，在陳絕緣體中被高度討論的拓撲相變大部分是藉由調整內在的材料參數所引發的，例如：交換耦合的強度。但在真實的應用當中，這並不是一個引發拓撲相變的實際方法。在此，我們表明拓撲相變可藉由調整以二維電子氣所形成的陳絕緣體之外在自由度-磁化方向來引發，其中二維電子氣具有Dresselhaus [001]自旋軌道耦合，且與其上方之磁性層有著交換耦合。透過解析的方法，我們表明該系統在面內磁化的情形下有著拓撲平庸的相，但當磁化偏離面內方向時則會發生拓撲相變。此解析的結果已進一步地利用非平衡態格林函數驗證。若將以上的拓撲相變和自旋轉移力矩結合，我們可以基於這種拓撲學和自旋電子學的前瞻性融合，設計出一種新穎的電晶體。最後我們將以上討論的陳絕緣體加上了s波超導體，形成了手性拓撲超導體。這種材料在拓撲量子計算上會有很重要的應用。

關鍵字

量子反常霍爾效應 ； 陳絕緣體 ； 祁-吳-張 模型 ； 拓撲相變 ； 非平衡態格林函數 ； 拓撲超導體

並列摘要

So far, the highly-discussed topological phase transitions in Chern insulators have mostly been induced by tuning an intrinsic material parameter such as the exchange coupling strength. But it is not a practical way to induce topological phase transitions in real applications. Here we show that the topological phase transitions can be induced by tuning the extrinsic degree of freedom, magnetization orientation, in a Chern insulaotr formed by a two-dimensional electron gas with Dresselhaus [001] spin-orbit coupling and an exchange coupling to a ferromagnetic overlayer. In an analytic way, we show that this system has a topologically trivial phase with in-plane magnetization but undergoes a topological phase transition when the magnetization is deviated from the in-plane direction. The analytic results are further confirmed by numerical nonequilibrium Green functions calculations. With the combination of this phase transition and spin-transfer torque, a novel transistor can be designed with this promising fusion of topology and spintronics. At last, we combine this Chern insulator with an s-wave superconductor, forming the chiral topological superconductor. It will have vital applications in topological quantum computation.

並列關鍵字

Quantum anomalous Hall effect ； Chern insulator ； Qi-Wu-Zhang model ； Topological phase transition ； Nonequilibrium Green functions ； Topological superconductor

參考文獻

[1] Jackiw, R. & Rebbi, C. Solitons with fermion number 1/2. Phys. Rev. D 13, 33983409 (1976).

[2] Haldane, F. D. M. Model for a quantum Hall effect without landau levels: Condensedmatter realization of the ”parity anomaly”. Phys. Rev. Lett. 61, 2015-2018 (1988).

[3] Hasan, M. Z. & Kane, C. L. Colloquium: Topological insulators. Rev. Mod. Phys. 82, 3045-3067 (2010).

[4] Qi, X.-L. & Zhang, S.-C. Topological insulators and superconductors. Rev. Mod.Phys. 83, 1057-1110 (2011).

[5] Majorana, E. Teoria simmetrica dell’elettrone e del positrone. Nuovo Cimento 14, 171 (1937).