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

We study the transport properties of a tight-binding model of noninteracting fermions with random hopping on the honeycomb lattice. At the particle-hole-symmetric chemical potential, the absence of diagonal disorder (random on-site 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-one-dimensional 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 $\ensuremath{\xi}/M$ ($M$ denotes the width of the sample) and the typical conductance display scaling behavior controlled by a crossover length scale that diverges with exponent $\ensuremath{\nu}\ensuremath{\approx}1.05(5)$ as the critical point is approached. However, for the plaquette dimerization pattern, we observe a relatively large exponent $\ensuremath{\nu}\ensuremath{\approx}1.55(5)$, revealing an apparent nonuniversality of the delocalization-localization transition in the BDI symmetry class.