467 research outputs found
Numerical study on Anderson transitions in three-dimensional disordered systems in random magnetic fields
The Anderson transitions in a random magnetic field in three dimensions are
investigated numerically. The critical behavior near the transition point is
analyzed in detail by means of the transfer matrix method with high accuracy
for systems both with and without an additional random scalar potential. We
find the critical exponent for the localization length to be with a strong random scalar potential. Without it, the exponent is
smaller but increases with the system sizes and extrapolates to the above value
within the error bars. These results support the conventional classification of
universality classes due to symmetry. Fractal dimensionality of the wave
function at the critical point is also estimated by the equation-of-motion
method.Comment: 9 pages, 3 figures, to appear in Annalen der Physi
Conductance plateau transitions in quantum Hall wires with spatially correlated random magnetic fields
Quantum transport properties in quantum Hall wires in the presence of
spatially correlated disordered magnetic fields are investigated numerically.
It is found that the correlation drastically changes the transport properties
associated with the edge state, in contrast to the naive expectation that the
correlation simply reduces the effect of disorder. In the presence of
correlation, the separation between the successive conductance plateau
transitions becomes larger than the bulk Landau level separation determined by
the mean value of the disordered magnetic fields. The transition energies
coincide with the Landau levels in an effective magnetic field stronger than
the mean value of the disordered magnetic field. For a long wire, the strength
of this effective magnetic field is of the order of the maximum value of the
magnetic fields in the system. It is shown that the effective field is
determined by a part where the stronger magnetic field region connects both
edges of the wire.Comment: 7 pages, 10 figure
Landau level broadening in graphene with long-range disorder -- Robustness of the n=0 level
Broadening of the Landau levels in graphene and the associated quantum Hall
plateau-to-plateau transition are investigated numerically. For correlated bond
disorder, the graphene-specific n=0 Landau level of the Dirac fermions becomes
anomalously sharp accompanied by the Hall transition exhibiting a
fixed-point-like criticality. Similarly anomalous behavior for the n=0 Landau
level is also shown to occur in correlated random magnetic fields, which
suggests that the anomaly is generic to disorders that preserve the chiral
symmetry.Comment: 4 pages, 5 figures, submitted to EP2DS-18 Conference proceeding
Quantum transport properties of two-dimensional systems in disordered magnetic fields with a fixed sign
Quantum transport in disordered magnetic fields is investigated numerically
in two-dimensional systems. In particular, the case where the mean and the
fluctuation of disordered magnetic fields are of the same order is considered.
It is found that in the limit of weak disorder the conductivity exhibits a
qualitatively different behavior from that in the conventional random magnetic
fields with zero mean. The conductivity is estimated by the equation of motion
method and by the two-terminal Landauer formula. It is demonstrated that the
conductance stays on the order of even in the weak disorder limit. The
present behavior can be interpreted in terms of the Drude formula. The
Shubnikov-de Haas oscillation is also observed in the weak disorder regime.Comment: 6 pages, 7 figures, to appear in Phys. Rev.
Chiral symmetry and fermion doubling in the zero-mode Landau levels of massless Dirac fermions with disorder
The effect of disorder on the Landau levels of massless Dirac fermions is
examined for the cases with and without the fermion doubling. To tune the
doubling a tight-binding model having a complex transfer integral is adopted to
shift the energies of two Dirac cones, which is theoretically proposed earlier
and realizable in cold atoms in an optical lattice. In the absence of the
fermion doubling, the Landau level is shown to exhibit an anomalous
sharpness even if the disorder is uncorrelated in space (i.e., large K-K'
scattering). This anomaly occurs when the disorder respects the chiral symmetry
of the Dirac cone.Comment: 3 pages, 2 figures, Proceedings of ICPS 2012, typos corrected, one
sentence added in section I
Magnetotransport in inhomogeneous magnetic fields
Quantum transport in inhomogeneous magnetic fields is investigated
numerically in two-dimensional systems using the equation of motion method. In
particular, the diffusion of electrons in random magnetic fields in the
presence of additional weak uniform magnetic fields is examined. It is found
that the conductivity is strongly suppressed by the additional uniform magnetic
field and saturates when the uniform magnetic field becomes on the order of the
fluctuation of the random magnetic field. The value of the conductivity at this
saturation is found to be insensitive to the magnitude of the fluctuation of
the random field. The effect of random potential on the magnetoconductance is
also discussed.Comment: 5 pages, 5 figure
Flavor Doubling and the Nature of Asymptopia
We consider the possibility that QCD with N flavors has a useful low-energy
description with 2N flavors. Specifically, we investigate a free theory of 2N
quarks. Although the free theory is U(N)_L X U(N)_R invariant, it admits a
larger U(2N) invariance. However, when the axial anomaly is accounted for in
the effective theory by a 't Hooft interaction, only SU(N)_L X SU(N)_R X U(1)_B
\subset U(2N) survives. There is however a residual discrete symmetry that is
not a symmetry of the QCD lagrangian. This S_2 subgroup of U(2N) has many
interesting properties. For instance, when explicit chiral symmetry breaking
effects are present, S_2 is broken unless \bar\theta=0 or pi. By expressing the
free theory on the light-front, we show that flavor doubling implies several
superconvergence relations in pion-hadron scattering. Implicit in the 2N-flavor
effective theory is a Regge trajectory with vacuum quantum numbers and unit
intercept whose behavior is constrained by S_2. In particular, S_2 implies that
forward pion-hadron scattering becomes purely elastic at high-energies, in good
agreement with experiment.Comment: 26 pages TeX, uses mtexsis.te
Unconventional conductance plateau transitions in quantum Hall wires with spatially correlated disorder
Quantum transport properties in quantum Hall wires in the presence of
spatially correlated random potential are investigated numerically. It is found
that the potential correlation reduces the localization length associated with
the edge state, in contrast to the naive expectation that the potential
correlation increases it. The effect appears as the sizable shift of quantized
conductance plateaus in long wires, where the plateau transitions occur at
energies much higher than the Landau band centers. The scale of the shift is of
the order of the strength of the random potential and is insensitive to the
strength of magnetic fields. Experimental implications are also discussed.Comment: 5 pages, 4 figure
Anderson transition of three dimensional phonon modes
Anderson transition of the phonon modes is studied numerically. The critical
exponent for the divergence of the localization length is estimated using the
transfer matrix method, and the statistics of the modes is analyzed. The latter
is shown to be in excellent agreement with the energy level statistics of the
disrodered electron system belonging to the orthogonal universality class.Comment: 2 pages and another page for 3 figures, J. Phys. Soc. Japa
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