5,005 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 for the
quantum Hall states, but 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 Landau band, the multifractal
properties of both the chiral and the split quantum Hall states are the same,
showing a parabolic distribution with .
In the absence of the constant magnetic field, the chiral critical state is
determined by
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
Quantum-Hall to insulator transition
The crossover from the quantum Hall regime to the Hall-insulator is
investigated by varying the strength of the diagonal disorder in a 2d
tight-binding model. The Hall and longitudinal conductivities and the behavior
of the critical states are calculated numerically. We find that with increasing
disorder the current carrying states close to the band center disappear first.
Simultaneously, the quantized Hall conductivity drops monotonically to zero
also from higher quantized values.Comment: 5 pages LaTeX2e, 5 ps-figures included. Proceedings SemiMag13,
Nijmegen 1998; to appear in Physica
Floating of critical states and the QH to insulator transition
The transition from the quantum Hall state to the insulator is considered for
non-interacting electrons in a two-dimensional disordered lattice model with
perpendicular magnetic field. Using correlated random disorder potentials the
floating up of the critical states can be observed in a similar way as in the
continuum model. Thus, the peculiar behaviour of the lattice models reported
previously originates in the special choice of uncorrelated random disorder
potentials.Comment: 4 pages incl. 4 eps-figures. Proceedings of SemiMag2000, Matsue,
Japan. To be published in Physica
Non-LTE treatment of molecules in the photospheres of cool stars
We present a technique to treat systems with very many levels, like
molecules, in non-LTE. This method is based on a superlevel formalism coupled
with rate operator splitting. Superlevels consist of many individual levels
that are assumed to be in LTE relative to each other. The usage of superlevels
reduces the dimensionality of the rate equations dramatically and, thereby,
makes the problem computationally more easily treatable. Our superlevel
formalism retains maximum accuracy by using direct opacity sampling (dOS) when
calculating the radiative transitions and the opacities. We developed this
method in order to treat molecules in cool dwarf model calculations in non-LTE.
Cool dwarfs have low electron densities and a radiation field that is far from
a black body radiation field, both properties may invalidate the conditions for
the common LTE approximation. Therefore, the most important opacity sources,
the molecules, need to be treated in non-LTE. As a case study we applied our
method to carbon monoxide. We find that our method gives accurate results since
the conditions for the superlevel method are very well met for molecules. Due
to very high collisional cross sections with hydrogen, and the high densities
of H_2 the population of CO itself shows no significant deviation from LTE.Comment: AASTeX v50, 35 pages including 12 figures, accepted by Ap
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