奈米圖形二維電子系統 Z2 拓樸性質之穩健性

Abstract

二維電子氣在奈米圖樣化的三角晶格位能中，低能量帶可發現相對論性零質量狄拉克費米子。另一方面，自旋軌道作用會在狄拉克點打開能隙並將類金屬轉換成Z2拓樸絕緣體。 根據這些現象，我們更進一步探討Z2拓樸性質在外加磁場下的穩健性。使用k∙p 理論寫下在磁場中低能量帶之等效Hamiltonian並解析上地計算能帶的Chern值。當只有平行平面方向磁場出現時，沿著垂直平面方向的向上自旋態與向下自旋態將被平行磁場耦合，而不再是良好的量子態。這些被混合的自旋態將破壞系統原本的Z2拓樸特性；如果再加上一個垂直平面方向的微小磁場，系統將可以回復Z2拓樸特性，這意味著Z2拓樸性質在適當外加磁場下的穩健性。

The relativistic massless Dirac fermions is found in the low energy bands of the two-dimensional electron gas subjected to triangular nano-patterned periodic potential. The spin-orbit interaction further introduces gap at Dirac points for the massless fermions and turns the semimetal into a Z2 topological insulator. Base on these facts, we investigate the robustness of the Z2 topological nature of the system under external magnetic field. The k∙p theory is employed to develop the effective Hamiltonian for the low energy bands with the presence of magnetic field. We analytically calculate the Chern numbers of the bands. For the presence of only in-plane magnetic field, the up and down spin along out-of-plane direction are no more good quantum states. The mixing of these states ruins the Z2 feature of the system. However, with arbitrary small out-of-plane magnetic field, the Z2 topological nature is restored meaning the robustness of its topology under external magnetic field.