Multifunctional stanene driven by a magnetic topological switch

We propose and analyze a novel, highly tunable magnetic topological switch that uses a single edge-localized magnetic perturbation to drive a stanene monolayer reversibly between three distinct phases: the quantum spin Hall state, a trivial band insulator, and a second-order topological insulator. By modestly varying the temperature T and the magnetization orientation θ, this single localized control element implements a minimalistic, experimentally accessible scheme that endows stanene nanoflake with genuine multifunctionality and direct relevance for topological device architectures. To substantiate this objective, we first investigate the bulk and nanoribbon geometries using the spin-Berry curvature, spin-Chern number, and Wilson loop, thereby exposing the limitations of these geometries in realizing the full multifunctionality of the proposed switch. We then show that multifunctionality emerges only in finite nanoflakes, where the spectral localizer captures both QSH-trivial and QSH-SOTI transitions through an effective gap closing and reopening governed by the edge-state penetration depth, together with the emergence of symmetry-protected fractional corner charges e/2 and e/4 across three inequivalent edge configurations. For each transition, we further examine the associated bulk-boundary correspondence principle.