The Δπ-Bond: An Exopolyhedral Three-Centered π-Bond Motif for Aromatic Self-Passivation in B₁₂-Based Two-Dimensional...

The successful exfoliation of free-standing covalent 2D materials from non-van der Waals solids critically depends on the intrinsic surface passivation to stabilize the dangling bonds created upon cleavage and hence requires a sizable semiconducting band gap, analogous to molecular systems. Ultrahard boron-rich borides built from polyhedral B₁₂ networks are reported to show an unusual propensity to form semiconducting 2D materials through both top-down and bottom-up synthetic approaches. However, the underlying origin of their stability and the mechanism of surface passivation remain unclear. Here, we show that the surfaces generated by breaking the interpolyhedral bonds between B₁₂ units prefer forming three-center two-electron (3c-2e) Δπ bonds, arising from lateral overlap between outward-pointing sp hybrids of a triangular set of boron atoms. Density functional calculations on molecular models and extended 2D sheets reveal that this Hückel-type 2D aromatic Δπ bonding effectively passivates dangling bonds and dominates the frontier electronic structure, acting as a functional group while sporting a modest energy gap. Furthermore, individual B₁₂ polyhedra can robustly host multiple Δπ bonds on their surface and exhibit conjugation effects reminiscent of organic π systems. These findings establish the Δπ bond as a unifying design principle to stabilize B₁₂-based 2D materials.