4,654 research outputs found

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

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 $\alpha(0)=2.14\pm 0.02$

### Landau level splitting due to graphene superlattices

The Landau level spectrum of graphene superlattices is studied using a
tight-binding approach. We consider non-interacting particles moving on a
hexagonal lattice with an additional one-dimensional superlattice made up of
periodic square potential barriers, which are oriented along the zig-zag or
along the arm-chair directions of graphene. In the presence of a perpendicular
magnetic field, such systems can be described by a set of one-dimensional
tight-binding equations, the Harper equations. The qualitative behavior of the
energy spectrum with respect to the strength of the superlattice potential
depends on the relation between the superlattice period and the magnetic
length. When the potential barriers are oriented along the arm-chair direction
of graphene, we find for strong magnetic fields that the zeroth Landau level of
graphene splits into two well separated sublevels, if the width of the barriers
is smaller than the magnetic length. In this situation, which persists even in
the presence of disorder, a plateau with zero Hall conductivity can be observed
around the Dirac point. This Landau level splitting is a true lattice effect
that cannot be obtained from the generally used continuum Dirac-fermion model.Comment: 12 pages, 9 figure

### Levitation of Current Carrying States in the Lattice Model for the Integer Quantum Hall Effect

The disorder driven quantum Hall to insulator transition is investigated for
a two-dimensional lattice model. The Hall conductivity and the localization
length are calculated numerically near the transition. For uncorrelated and
weakly correlated disorder potentials the current carrying states are
annihilated by the negative Chern states originating from the band center. In
the presence of correlated disorder potentials with correlation length larger
than approximately half the lattice constant the floating up of the critical
states in energy without merging is observed. This behavior is similar to the
levitation scenario proposed for the continuum model.Comment: 4 pages incl. 4 eps-figures. Published versio

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