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We numerically compute the density of states (DOS) of interacting disorderedzigzag graphene nanoribbon (ZGNR) having midgap states showing $e/2$ fractionaledge charges. The computed Hartree-Fock DOS is linear at the critical disorderstrength where the gap vanishes. This implies an $I\mbox{-}V$ curve of$I\propto V^2$. Thus, $I\mbox{-}V$ curve measurement may yield evidence offractional charges in interacting disordered ZGNR. We show that even a weakdisorder potential acts as a singular perturbation on zigzag edge electronicstates, producing drastic changes in the energy spectrum. Spin-chargeseparation and fractional charges play a key role in the reconstruction of edgeantiferromagnetism. Our results show that an interacting disordered ZGNR is atopologically ordered Mott-Anderson insulator.

Topologically ordered zigzag nanoribbon: $e/2$ fractional edge charge, spin-charge separation, and ground state degeneracy