Disorder-driven splitting of the conductance peak at the Dirac point in graphene

Abstract

The electronic properties of a bricklayer model, which shares the same topology as the hexagonal lattice of graphene, are investigated numerically. We study the influence of random magnetic-field disorder in addition to a strong perpendicular magnetic field. We found a disorder-driven splitting of the longitudinal conductance peak within the narrow lowest Landau band near the Dirac point. The energy splitting follows a relation which is proportional to the square root of the magnetic field and linear in the disorder strength. We calculate the scale invariant peaks of the two-terminal conductance and obtain the critical exponents as well as the multifractal properties of the chiral and quantum Hall states. We found approximate values Ϸ 2.5 for the quantum Hall states but = 0.33Ϯ 0.1 for the divergence of the correlation length of the chiral state at E = 0 in the presence of a strong magnetic field. Within the central n = 0 Landau band, the multifractal properties of both the chiral and the split quantum Hall states are the same, showing a parabolic f͓␣͑s͔͒ distribution with ␣͑0͒ = 2.27Ϯ 0.02. In the absence of the constant magnetic field, the chiral critical state is determined by ␣͑0͒ = 2.14Ϯ 0.02.

Narrow depression in the density of states at the Dirac point in disordered graphene

“…In the present study, the two-dimensional honeycomb lattice responsible for the peculiar electronic properties of graphene is replaced by a bricklayer model 8,9,18 which shares the same topology as the hexagonal lattice. The bricklayer lattice is bi-partite and consists of two sublattices that can be constructed by rectangular unit cells of size 2a × a placed along the x-direction.…”

“…There is also an additional narrow structure discernible around E = 0 and this was previously attributed to originate from the chiral critical eigenstates. 18 In order to scrutinize this special feature, more than 10 4 disorder realizations were calculated. Thereby, a binwidth of about 5 × 10 −7 becomes possible leading to an enhanced energy resolution.…”

“…14 Yet, which type of disorder is encountered in real samples is still completely unclear or only partly known in some special cases. This lack of knowledge is particularly unfortunate as the definite type of disorder entirely determines the physical properties, 15,16,17,18,19,20,21 e.g., leading to complete Anderson localization in the case of short range electrostatic scattering potentials via chiral symmetry breaking and scattering between valleys. 22,23 For disordered systems, even the single particle density of states (DOS) near the Dirac point remains still under debate.…”

“…18 It was found that with increasing disorder, the critical energies where the plateau transitions of the Hall conductivity take place, move apart. This splitting of the central conductance peak unveiled the existence of an extra chiral quantum phase transition occurring at zero energy with critical properties that differ from those of the quantum Hall transitions.…”

“…This splitting of the central conductance peak unveiled the existence of an extra chiral quantum phase transition occurring at zero energy with critical properties that differ from those of the quantum Hall transitions. 18 In the present work, the single particle density of states is calculated numerically for the same bricklayer lattice model. The presumed ripple disorder is modeled by a spatially varying random magnetic flux with zero mean, pointing perpendicular to the two-dimensional lattice.…”