Response of quantum spin Hall insulators to Zeeman fields, and device design based on stanene

The nontrivial topology of materials has been one of the keys for breaking through to a new stage of electronics involving phenomena such as topologically protected quantum spin Hall (QSH) states and quantum anomalous Hall (QAH) states. In this work, we study the Kane-Mele model with next-nearest-neighbor Rashba spin-orbit coupling (SOC), which accurately describes the QSH effect of two-dimensional group IV A materials. By investigating electronic structures with different SOCs and Zeeman fields, we obtain various phase transitions and plot rich phase diagrams where a time-reversal-symmetry-broken QSH insulator and three types of QAH insulators are identified based on calculations of topological invariants, including total and spin Chern numbers and Wannier function centers. In addition, the edge modes and spin texture within the bulk gap are also nontrivial. Based on the results of the model, we also study a real QSH material, stanene, with a large bulk gap and propose a scheme based on its transport properties to design a spin-resolved filter.