Band-center metal-insulator transition in bond-disordered graphene

Abstract

We study the transport properties of a tight-binding model of non-interacting fermions with random hopping on the honeycomb lattice. At the particle-hole symmetric chemical potential, the absence of diagonal disorder (random onsite potentials) places the system in the well-studied chiral orthogonal universality class of disordered fermion problems, which are known to exhibit both a critical metallic phase and a dimerization-induced localized phase. Here, our focus is the behavior of the two-terminal conductance and the Lyapunov spectrum in quasi-1D geometry near the dimerization-driven transition from the metallic to the localized phase. For a staggered dimerization pattern on the square and honeycomb lattices, we find that the renormalized localization length $\xi /M$ ($M$ denotes the width of the sample) and the typical conductance display scaling behavior controlled by a crossover length-scale that diverges with exponent $\nu \approx 1.05(5)$ as the critical point is approached. However, for the plaquette dimerization pattern, we observe a relatively large exponent $\nu \approx 1.55(5)$ revealing an apparent non-universality of the delocalization-localization transition in the BDI symmetry class.

8+3 pages, 7 figures

References in corpus (5)

• Anderson Transitions
• Density of states in graphene with vacancies: midgap power law and frozen multifractality
• Density of states in a two-dimensional chiral metal with vacancies
• Metal-insulator transition in a 2D system of chiral unitary class
• Two parameter scaling in the crossover from symmetry class BDI to AI

Cited by in corpus (1)

• Critical States of Fermions with ${\mathbb{Z}}_2$ Flux Disorder