Disordered graphene ribbons as topological multicritical systems

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