First principles calculations of electric field driven topological phase transitions in silicene, germanene and stanene.

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 fieldat which these transitions occur remains challenging, with tight-binding (TB) models often underestimating these values. Here, we present a first-principles framework that combines density-functional theory, maximally localized Wannier functions, and evolution of the Wannier charge centers to accurately characterize TPTs in silicene, germanene, and stanene through thetopological invariant. In contrast to earlier work, at each electric-field strength we run fully self-consistentab initiosimulations 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 TB Hamiltonian at each electric field strength, which then enables a gauge-invariant calculation of thetopological invariant. This methodology yields significantly more accurate numerical predictions of-andfor silicene and germanene, respectively-and provides deeper insight into the interplay between electronic structure and topological order. 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.