Disordered Graphene Ribbons as Topological Multicritical Systems

TL;DR

This paper studies disordered zigzag graphene ribbons at a topological multicritical point, revealing universal delocalized states and Dyson singularity in the density of states, with non-universal localization length critical exponents.

Contribution

It demonstrates how chiral symmetry-preserving disorder affects the topological multicritical point in graphene ribbons, highlighting universal and non-universal critical behaviors.

Findings

Delocalized states with diverging localization length at zero energy.

Universal Dyson singularity in the density of states.

Non-universal zero-energy localization length critical exponent.

Abstract

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 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 {\em 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 $W$.