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

TL;DR

This study numerically investigates how random magnetic-field disorder causes a splitting of the conductance peak at the Dirac point in graphene-like systems, revealing disorder-dependent energy splitting and critical properties of quantum Hall states.

Contribution

It introduces a detailed numerical analysis of disorder effects on conductance peaks and critical states in a graphene-like lattice under magnetic fields, highlighting a disorder-driven splitting mechanism.

Findings

Disorder causes a splitting of the conductance peak near the Dirac point.

The energy splitting scales with the square root of magnetic field and linearly with disorder strength.

Critical exponents and multifractal properties of quantum Hall and chiral states are characterized.

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 $\nu\approx 2.5$ for the quantum Hall states, but $\nu=0.33\pm 0.1$ 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 $f[\alpha(s)]$ distribution with $\alpha(0)=2.27\pm 0.02$. In the absence of the constant magnetic field, the chiral critical state is determined by $\alpha(0)=2.14\pm 0.02$.