Designing a polymerized phenalenyl tessellation molecule to realize a super-honeycomb antiferromagnetic S = 3/2 spin system

In a multiply hydrogenated polymer of phenalenyl tessellation molecules (PTMs), spatially overlapping zero modes appear, and three spin-aligned electron spins per PTM are generated through direct exchange interactions in the strongly correlated electron system. This interaction was used to design a two-dimensional (2D) $S=3\mathrm{/}2$ Heisenberg spin system on a honeycomb lattice. Simulations of the electronic structure using density functional theory with the Wannierization method revealed an array of nonbonding molecular orbitals (zero modes) in the hydrogenated nanographene structure. Our analysis of the onsite interaction strength indicated that each zero mode was half-filled with a spin-active electron owing to electron correlation effects. The low-energy subspace of the resulting zero mode-tight-binding model suggests the formation of a 2D antiferromagnetic $S=3\mathrm{/}2$ Heisenberg system with an entangled quantum spin ground state.