Disordered graphene ribbons as topological multicritical systems

Saumitran Kasturirangan, Alex Kamenev, Fiona J. Burnell

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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.

Original languageEnglish (US)
Article number184206
JournalPhysical Review B
Issue number18
StatePublished - Nov 1 2022

Bibliographical note

Funding Information:
This work was supported primarily by the National Science Foundation through the University of Minnesota MRSEC under Award No. DMR-2011401. F.J.B. acknowledges the financial support of NSF: DMR-1928166 and the Carnegie corporation of New York. A.K. was supported by the NSF Grant No. DMR-2037654.

Publisher Copyright:
© 2022 American Physical Society.

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