硅烯、锗烯和锡烯中电场驱动拓扑相变的第一性原理计算
First principles calculations of electric-field-driven topological phase transitions in silicene, germanene and stanene
AI总结：
本文通过第一性原理计算，结合DFT和万尼尔函数，精确预测硅烯和锗烯的临界电场，显著改进拓扑相变边界的定量预测。
AI中文摘要：
二维拓扑材料的出现，特别是被称为硅烯、锗烯和锡烯的第14族单层材料，为下一代纳米电子学和自旋电子学开辟了有前景的途径。它们的翘曲蜂窝结构和强自旋轨道耦合允许通过垂直电场进行带隙工程，从而导致从非平凡到平凡绝缘态的拓扑相变（TPTs）。然而，精确确定这些转变发生的临界电场 $E_z^{\text{cr}}$ 仍然具有挑战性，紧束缚模型往往低估这些值。在这里，我们提出了一个第一性原理框架，该框架结合了密度泛函理论（DFT）、最大局域化万尼尔函数和万尼尔电荷中心（WCC）的演化，通过 $\mathbb{Z}_2$ 拓扑不变量精确表征硅烯、锗烯和锡烯中的拓扑相变。与早期工作相比，我们在每个电场强度下运行完全自洽的从头算模拟，以获得屏蔽电子结构，同时考虑材料和离子的介电响应。从这些收敛结果中，我们在每个电场强度下构建万尼尔紧束缚哈密顿量，从而能够进行 $\mathbb{Z}_2$ 拓扑不变量的规范不变计算。该方法产生了对 $E_z^{\text{cr}}$ 显著更准确的数值预测，硅烯和锗烯分别为 $0.020$ 和 $0.250$ V/Å。与先前方法相比，我们的框架在预测拓扑相边界方面提供了显著的定量改进，这对于指导基于二维材料的拓扑场效应晶体管和静电控制量子器件的设计至关重要。
英文摘要：
The emergence of two-dimensional topological materials, particularly the group-14 monolayers known as silicene, germanene, and stanene has opened promising pathways for next-generation nanoelectronics and spintronics. Their buckled honeycomb structure and strong spin-orbit coupling allow for bandgap engineering via a perpendicular electric field, leading to topological phase transitions (TPTs) from non-trivial to trivial insulating states. However, precise determination of the critical electric field $E_z^{\text{cr}}$ at which these transitions occur remains challenging, with tight-binding models often underestimating these values. Here, we present a first-principles framework that combines density-functional theory (DFT), maximally localized Wannier functions, and evolution of the Wannier charge centers (WCC) to accurately characterize TPTs in silicene, germanene, and stanene through the $\mathbb{Z}_2$ topological invariant. In contrast to earlier work, at each electric-field strength we run fully self-consistent ab initio simulations to obtain the screened electronic structure, accounting for the material's dielectric response from both electrons and ions. From these converged results we construct a Wannier tight-binding Hamiltonian at each electric field strength, which then enables a gauge-invariant calculation of the $\mathbb{Z}_2$ topological invariant. This methodology yields significantly more accurate numerical predictions of $E_z^{\text{cr}}$, $0.020$ and $0.250$ V/Å for silicene and germanene, respectively. Compared to previous approaches, our framework delivers a marked quantitative improvement for predicting topological phase boundaries, essential for guiding the design of topological field-effect transistors and electrostatically controlled quantum devices based on two-dimensional materials.
