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.

arXiv comment8+3 pages, 7 figures

References in corpus (21)

• Classification of topological quantum matter with symmetries
• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Anderson Transitions
• Kwant: a software package for quantum transport
• Corrections to scaling at the Anderson transition
• Numerical Analysis of the Anderson Localization
• Particle-hole symmetric localization in two dimensions
• Reconciling Conductance Fluctuations and the Scaling Theory of Localization
• Disordered Critical Wave functions in Random Bond Models in Two Dimensions -- Random Lattice Fermions at $E=0$ without Doubling
• Density of states in coupled chains with off-diagonal disorder
• Density of states for the $\pi$-flux state with bipartite real random hopping only: A weak disorder approach
• Metal-insulator transition in 2D random fermion systems of chiral symmetry classes
• Fokker-Planck equations and density of states in disordered quantum wires
• Density of states in graphene with vacancies: midgap power law and frozen multifractality
• Density of states in a two-dimensional chiral metal with vacancies
• Network models for localisation problems belonging to the chiral symmetry classes
• Chalker scaling, level repulsion, and conformal invariance in critically delocalized quantum matter: Disordered topological superconductors and artificial graphene
• Vacancy-induced low-energy states in undoped graphene
• Generalized Dyson model: nature of zero mode and its implication in dynamics
• 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