791 research outputs found
Integer quantum Hall effect and Hofstadter's butterfly spectra in three-dimensional metals in external periodic modulations
We propose that Hofstadter's butterfly accompanied by quantum Hall effect
that is similar to those predicted to occur in 3D tight-binding systems by
Koshino {\it et al.} [Phys. Rev. Lett. {\bf 86}, 1062 (2001)] can be realized
in an entirely different system -- 3D metals applied with weak external
periodic modulations (e.g., acoustic waves). Namely, an effect of two periodic
potentials interferes with Landau's quantization due to an applied magnetic
field \Vec{B}, resulting generally in fractal energy gaps as a function of
the tilting angle of \Vec{B}, for which the accompanying quantized Hall
tensors are computed. The phenomenon arises from the fact that, while the
present system has a different physical origin for the butterfly from the 3D
tight-binding systems, the mathematical forms are remarkably equivalent.Comment: 4 pages, 2 figure
Hall plateau diagram for the Hofstadter butterfly energy spectrum
We extensively study the localization and the quantum Hall effect in the
Hofstadter butterfly, which emerges in a two-dimensional electron system with a
weak two-dimensional periodic potential. We numerically calculate the Hall
conductivity and the localization length for finite systems with the disorder
in general magnetic fields, and estimate the energies of the extended levels in
an infinite system. We obtain the Hall plateau diagram on the whole region of
the Hofstadter butterfly, and propose a theory for the evolution of the plateau
structure with increasing disorder. There we show that a subband with the Hall
conductivity has separated bunches of extended levels, at least
for an integer . We also find that the clusters of the subbands with
identical Hall conductivity, which repeatedly appear in the Hofstadter
butterfly, have a similar localization property.Comment: 9 pages, 12 figure
Metal insulator transition in modulated quantum Hall systems
The quantum Hall effect is studied numerically in modulated two-dimensional
electron systems in the presence of disorder. Based on the scaling property of
the Hall conductivity as well as the localization length, the critical energies
where the states are extended are identified. We find that the critical
energies, which are distributed to each of the subbands, combine into one when
the disorder becomes strong, in the way depending on the symmetry of the
disorder and/or the periodic potential.Comment: 4 pages, 4 figures, to appear in Physica
Duality and integer quantum Hall effect in isotropic 3D crystals
We show here a series of energy gaps as in Hofstadter's butterfly, which have
been shown to exist by Koshino et al [Phys. Rev. Lett. 86, 1062 (2001)] for
anisotropic three-dimensional (3D) periodic systems in magnetic fields
\Vec{B}, also arise in the isotropic case unless \Vec{B} points in
high-symmetry directions. Accompanying integer quantum Hall conductivities
can, surprisingly, take values
even for a fixed direction of \Vec{B}
unlike in the anisotropic case. We can intuitively explain the high-magnetic
field spectra and the 3D QHE in terms of quantum mechanical hopping by
introducing a ``duality'', which connects the 3D system in a strong \Vec{B}
with another problem in a weak magnetic field .Comment: 7 pages, 6 figure
Electronic transport properties of few-layer graphene materials
Since the discovery of graphene -a single layer of carbon atoms arranged in a
honeycomb lattice - it was clear that this truly is a unique material system
with an unprecedented combination of physical properties. Graphene is the
thinnest membrane present in nature -just one atom thick- it is the strongest
material, it is transparent and it is a very good conductor with room
temperature charge mobilities larger than the typical mobilities found in
silicon. The significance played by this new material system is even more
apparent when considering that graphene is the thinnest member of a larger
family: the few-layer graphene materials. Even though several physical
properties are shared between graphene and its few-layers, recent theoretical
and experimental advances demonstrate that each specific thickness of few-layer
graphene is a material with unique physical properties.Comment: 26 pages, 8 figure
Trigonal warping and Berry’s phase Npi in ABC-stacked multilayer graphene.
The electronic band structure of ABC-stacked multilayer graphene is studied within an effective mass approximation. The electron and hole bands touching at zero energy support chiral quasiparticles characterized by Berry’s phase Nπ for N-layers, generalizing the low-energy band structure of monolayer and bilayer graphene. We investigate the trigonal-warping deformation of the energy bands and show that the Lifshitz transition, in which the Fermi circle breaks up into separate parts at low energy, reflects Berry’s phase Nπ. It is particularly prominent in trilayers, N = 3, with the Fermi circle breaking into three parts at a relatively large energy that is related to next-nearestlayer coupling. For N = 3, we study the effects of electrostatic potentials which vary in the stacking direction, and find that a perpendicular electric field, as well as opening an energy gap, strongly enhances the trigonal-warping effect. In magnetic fields, the N = 3 Lifshitz transition is manifested as a coalescence of Landau levels into triply-degenerate levels
Magnetic field screening and mirroring in graphene
The orbital magnetism in spatially varying magnetic fields is studied in
monolayer graphene within the effective mass approximation. We find that,
unlike the conventional two-dimensional electron system, graphene with small
Fermi wave number k_F works as a magnetic shield where the field produced by a
magnetic object placed above graphene is always screened by a constant factor
on the other side of graphene. The object is repelled by a diamagnetic force
from the graphene, as if there exists its mirror image with a reduced amplitude
on the other side of graphene. The magnitude of the force is much greater than
that of conventional two-dimensional system. The effect disappears with the
increase of k_F.Comment: 5 pages, 3 figure
Electronic structure of an electron on the gyroid surface, a helical labyrinth
Previously reported formulation for electrons on curved periodic surfaces is
used to analyze the band structure of an electron bound on the gyroid surface
(the only triply-periodic minimal surface that has screw axes). We find that an
effect of the helical structure appears as the bands multiply sticking together
on the Brillouin zone boundaries. We elaborate how the band sticking is lifted
when the helical and inversion symmetries of the structure are degraded. We
find from this that the symmetries give rise to prominent peaks in the density
of states.Comment: RevTeX, 4 pages, 6 figure
Disentanglement in a quantum critical environment
We study the dynamical process of disentanglement of two qubits and two
qutrits coupled to an Ising spin chain in a transverse field, which exhibits a
quantum phase transition. We use the concurrence and negativity to quantify
entanglement of two qubits and two qutrits, respectively. Explicit connections
between the concurrence (negativity) and the decoherence factors are given for
two initial states, the pure maximally entangled state and the mixed Werner
state. We find that the concurrence and negativity decay exponentially with
fourth power of time in the vicinity of critical point of the environmental
system.Comment: 8 pages, 6 figure
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