Disordered graphene ribbons as topological multicritical systems

The low-energy spectrum of a zigzag graphene ribbon contains two gapless bands with highly nonlinear dispersion, ϵ(k)=±|π-k|W, where W is the width of the ribbon. The corresponding states are located at the two opposite zigzag edges. Their presence reflects the fact that the clean ribbon is a quasi-one-dimensional system naturally fine-tuned to the topological multicritical point. This quantum critical point separates a topologically trivial phase from the topological one with the index W. Here we investigate the influence of the (chiral) symmetry-preserving disorder on such a multicritical point. We show that the system harbors delocalized states with the localization length diverging at zero energy in a manner consistent with the W=1 critical point. The same is true regarding the density of states (DOS), which exhibits the universal Dyson singularity, despite the clean DOS being substantially dependent on W. On the other hand, the zero-energy localization length critical exponent, associated with the lattice staggering, is not universal and depends on the topological index W.