Theoretical Analysis on Pseudo-Degenerate Zero-Energy Modes in   Vacancy-Centered Hexagonal Armchair Nanographene
  Deriving mathematical expressions of two zero modes for a $\pi$-band tight-binding model, we identify a class of bipartite graphs having the same number of subgraph sites, where each graph represents one of the quasi-hexagonal nanographene molecule with a center vacancy (VANG). Indeed, in a VANG molecule, C$_{60}$H$_{24}$, showing stability in a density-functional simulation at the highest occupied level, there appear two pseudo-degenerate zero modes, a vacancy-centered quasi-localized zero mode, and extending zero mode with a $\sqrt{3} \times \sqrt{3}$ structure. Since there is a finite energy gap between these two zero-energy modes and the other modes, low-lying states composed of quasi-degenerate zero modes appear as magnetic multiplets. Thus, the unique magnetic characteristics derived in our theory are expected to hold for synthesized VANG molecules in reality. 
Naoki Morishita, Gagus Ketut Sunnardianto, Satoaki Miyao, Koichi   Kusakabe
cond-mat.mes-hall cond-mat.mtrl-sci