343 research outputs found
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
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
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
Critical wave-packet dynamics in the power-law bond disordered Anderson Model
We investigate the wave-packet dynamics of the power-law bond disordered
one-dimensional Anderson model with hopping amplitudes decreasing as
. We consider the critical case ().
Using an exact diagonalization scheme on finite chains, we compute the
participation moments of all stationary energy eigenstates as well as the
spreading of an initially localized wave-packet. The eigenstates
multifractality is characterized by the set of fractal dimensions of the
participation moments. The wave-packet shows a diffusive-like spread developing
a power-law tail and achieves a stationary non-uniform profile after reflecting
at the chain boundaries. As a consequence, the time-dependent participation
moments exhibit two distinct scaling regimes. We formulate a finite-size
scaling hypothesis for the participation moments relating their scaling
exponents to the ones governing the return probability and wave-function
power-law decays
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
Critical conductance of two-dimensional chiral systems with random magnetic flux
The zero temperature transport properties of two-dimensional lattice systems
with static random magnetic flux per plaquette and zero mean are investigated
numerically. We study the two-terminal conductance and its dependence on
energy, sample size, and magnetic flux strength. The influence of boundary
conditions and of the oddness of the number of sites in the transverse
direction is also studied. We confirm the existence of a critical chiral state
in the middle of the energy band and calculate the critical exponent nu=0.35
+/- 0.03 for the divergence of the localization length. The sample averaged
scale independent critical conductance _c turns out to be a function of the
amplitude of the flux fluctuations whereas the variance of the respective
conductance distributions appears to be universal. All electronic states
outside of the band center are found to be localized.Comment: to appear in Phys. Rev.
Metal-insulator transitions in anisotropic 2d systems
Several phenomena related to the critical behaviour of non-interacting
electrons in a disordered 2d tight-binding system with a magnetic field are
studied. Localization lengths, critical exponents and density of states are
computed using transfer matrix techniques. Scaling functions of isotropic
systems are recovered once the dimension of the system in each direction is
chosen proportional to the localization length. It is also found that the
critical point is independent of the propagation direction, and that the
critical exponents for the localization length for both propagating directions
are equal to that of the isotropic system (approximately 7/3). We also
calculate the critical value of the scaling function for both the isotropic and
the anisotropic system. It is found that the isotropic value equals the
geometric mean of the two anisotropic values. Detailed numerical studies of the
density of states for the isotropic system reveals that for an appreciable
amount of disorder the critical energy is off the band center.Comment: 6 pages RevTeX, 6 figures included, submitted to Physical Review
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