Orbital-Ordering-Induced Two-Dimensional Valence Bond Solid in Nitride/Boron[3]Triangulene Crystals

The realization of the two-dimensional (2D) valence bond solid (VBS) is one frontier research topic in surface science. In this work, utilizing first-principles-based many-body calculations, we propose a realistic material platform to achieve this unique phase in nitrogen/boron-[3]triangulene crystals. It is described by the four-band honeycomb lattice at 3/4 or 1/4 filling, and Coulomb interactions drive it into a stable 2D VBS phase with three equivalent configurations linked by C3 symmetry, resulting from the special px,y-type orbital ordering. The spatial distribution of charge density, triplon excitations, and fractional edge spins provides several hallmark experimental signatures to identify it, which can be detected by state-of-the-art scanning tunneling microscope measurements. Our results introduce orbital freedom to engineer the 2D VBS, further enriching the orbital-dominated quantum magnetism in π-conjugated covalent-organic frameworks.