奈米圖形二維電子系統 Z2 拓樸性質之穩健性

Abstract

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.