Layer-polarized corner states in two-dimensional bilayer second-order topological insulators induced by electric field

Two-dimensional (2D) second-order topological insulators (SOTIs) with corner states have recently attracted significant interest. It is fascinating to explore the coupling of corner states with additional degrees of freedom. Here, we propose that layer-polarized corner states can be induced by a perpendicular electric field in the AA-stacking bilayer 2D SOTIs. Our result reveals that the transition between non-layer-polarized and layer-polarized corner states depends on the interlayer exchange symmetry, which can be controlled by the perpendicular electric field. This finding is further verified in two types of SOTIs: bilayer modified Kane-Mele model and ${C}_{n}$-symmetric SOTIs. In contrast to the bilayer modified Kane-Mele model, magnetic ${C}_{n}$-symmetric SOTIs are predicted to exhibit corner states that are not only layer polarized but also additionally spin-polarized, as exemplified by 1T-${\mathrm{NiCl}}_{2}$. Based on the first-principles calculations and tight-binding (TB) model, we predict that ferromagnetic (FM) single-layer 1T-${\mathrm{NiCl}}_{2}$ exhibits ${C}_{3}$-symmetric corner states with nontrivial fractional charge in both spin channels. Notably, in the bilayer ${\mathrm{NiCl}}_{2}$ with antiferromagnetic (AFM) ground state, applying a perpendicular electric field drives the transition of the corner states from a spin- and layer-degenerate state to a spin- and layer-polarized state. Reversing the electric field direction simultaneously switches both the spin and layer polarizations. Finally, layer-polarized corner states are also confirmed in the nonmagnetic bilayer hexagonal SOTI. These results indicate that electrically tunable layer-polarized corner states could be realized in a variety of bilayer SOTIs and interlayer magnetic configurations. Our work offers a strategy for designing layer-polarized corner states in 2D SOTIs, which could enhance their potential applications in topological electronic devices.