18 research outputs found
Local and average fields inside surface-disordered waveguides: Resonances in the one-dimensional Anderson localization regime
We investigate the one-dimensional propagation of waves in the Anderson
localization regime, for a single-mode, surface disordered waveguide. We make
use of both an analytical formulation and rigorous numerical simulation
calculations. The occurrence of anomalously large transmission coefficients for
given realizations and/or frequencies is studied, revealing huge field
intensity concentration inside the disordered waveguide. The analytically
predicted s-like dependence of the average intensity, being in good agreement
with the numerical results for moderately long systems, fails to explain the
intensity distribution observed deep in the localized regime. The average
contribution to the field intensity from the resonances that are above a
threshold transmission coefficient is a broad distribution with a large
maximum at/near mid-waveguide, depending universally (for given ) on the
ratio of the length of the disorder segment to the localization length,
. The same universality is observed in the spatial distribution of the
intensity inside typical (non-resonant with respect to the transmission
coefficient) realizations, presenting a s-like shape similar to that of the
total average intensity for close to 1, which decays faster the lower
is . Evidence is given of the self-averaging nature of the random
quantity . Higher-order moments of the intensity are
also shown.Comment: 9 pages, 9 figure
Scaling of the localization length in linear electronic and vibrational systems with long-range correlated disorder
The localization lengths of long-range correlated disordered chains are
studied for electronic wavefunctions in the Anderson model and for vibrational
states. A scaling theory close to the band edge is developed in the Anderson
model and supported by numerical simulations. This scaling theory is mapped
onto the vibrational case at small frequencies. It is shown that for small
frequencies, unexpectateley the localization length is smaller for correlated
than for uncorrelated chains.Comment: to be published in PRB, 4 pages, 2 Figure
A Tale of Two Fractals: The Hofstadter Butterfly and The Integral Apollonian Gaskets
This paper unveils a mapping between a quantum fractal that describes a
physical phenomena, and an abstract geometrical fractal. The quantum fractal is
the Hofstadter butterfly discovered in 1976 in an iconic condensed matter
problem of electrons moving in a two-dimensional lattice in a transverse
magnetic field. The geometric fractal is the integer Apollonian gasket
characterized in terms of a 300 BC problem of mutually tangent circles. Both of
these fractals are made up of integers. In the Hofstadter butterfly, these
integers encode the topological quantum numbers of quantum Hall conductivity.
In the Apollonian gaskets an infinite number of mutually tangent circles are
nested inside each other, where each circle has integer curvature. The mapping
between these two fractals reveals a hidden threefold symmetry embedded in the
kaleidoscopic images that describe the asymptotic scaling properties of the
butterfly. This paper also serves as a mini review of these fractals,
emphasizing their hierarchical aspects in terms of Farey fractions
Self-similarity and novel sample-length-dependence of conductance in quasiperiodic lateral magnetic superlattices
We study the transport of electrons in a Fibonacci magnetic superlattice
produced on a two-dimensional electron gas modulated by parallel magnetic field
stripes arranged in a Fibonacci sequence. Both the transmission coefficient and
conductance exhibit self-similarity and the six-circle property. The presence
of extended states yields a finite conductivity at infinite length, that may be
detected as an abrupt change in the conductance as the Fermi energy is varied,
much as a metal-insulator transition. This is a unique feature of transport in
this new kind of structure, arising from its inherent two-dimensional nature.Comment: 9 pages, 5 figures, revtex, important revisions made. to be published
in Phys. Rev.
Resonant scattering on impurities in the Quantum Hall Effect
We develop a new approach to carrier transport between the edge states via
resonant scattering on impurities, which is applicable both for short and long
range impurities. A detailed analysis of resonant scattering on a single
impurity is performed. The results are used for study of the inter-edge
transport by multiple resonant hopping via different impurities' sites. It is
shown that the total conductance can be found from an effective Schroedinger
equation with constant diagonal matrix elements in the Hamiltonian, where the
complex non-diagonal matrix elements are the amplitudes of a carrier hopping
between different impurities. It is explicitly demonstrated how the complex
phase leads to Aharonov-Bohm oscillations in the total conductance. Neglecting
the contribution of self-crossing resonant-percolation trajectories, one finds
that the inter-edge carrier transport is similar to propagation in
one-dimensional system with off-diagonal disorder. We demonstrated that each
Landau band has an extended state , while all other states are
localized. The localization length behaves as .Comment: RevTex 41 pages; 3 Postscript figure on request; Final version
accepted for publication in Phys. Rev. B. A new section added contained a
comparison with other method
Tunneling from a correlated 2D electron system transverse to a magnetic field
We show that, in a magnetic field parallel to the 2D electron layer, strong
electron correlations change the rate of tunneling from the layer
exponentially. It results in a specific density dependence of the escape rate.
The mechanism is a dynamical Mossbauer-type recoil, in which the Hall momentum
of the tunneling electron is partly transferred to the whole electron system,
depending on the interrelation between the rate of interelectron momentum
exchange and the tunneling duration. We also show that, in a certain
temperature range, magnetic field can enhance rather than suppress the
tunneling rate. The effect is due to the magnetic field induced energy exchange
between the in-plane and out-of-plane motion. Magnetic field can also induce
switching between intra-well states from which the system tunnels, and a
transition from tunneling to thermal activation. Explicit results are obtained
for a Wigner crystal. They are in qualitative and quantitative agreement with
the relevant experimental data, with no adjustable parameters.Comment: 16 pages, 9 figure
Quantum Hall Effect in Three-dimensional Field-Induced Spin Density Wave Phases with a Tilted Magnetic Field
The quantum Hall effect in the three-dimensional anisotropic tight-binding
electrons is investigated in the field-induced spin density wave phases with a
magnetic field tilted to any direction. The Hall conductivity,
and , are shown to be quantized as a function of the wave vector
of FISDW, while stays zero, where is the most conducting
direction and and are perpendicular to .Comment: 18 pages, REVTeX 3.0, 1 figure is available upon request, to be
published in Physical Review
Magnetothemopower study of quasi two-dimensional organic conductor -(BEDT-TTF)KHg(SCN)
We have used a low-frequency magneto-thermopower (MTEP) method to probe the
high magnetic field ground state behavior of
-(BEDT-TTF)KHg(SCN) along all three principal crystallographic
axes at low temperatures. The thermopower tensor coefficients (
and ) have been measured to 30 T, beyond the anomalous low temperature,
field-induced transition at 22.5 T. We find a significant anisotropy in the
MTEP signal, and also observe large quantum oscillations associated with the de
Haas - van Alphen effect. The anisotropy indicates that the ground state
properties are clearly driven by mechanisms that occur along specific
directions for the in-plane electronic structure. Both transverse and
longitudinal magnetothermopower show asymptotic behavior in field, which can be
explained in terms of magnetic breakdown of compensated closed orbits.Comment: 9 pages, 10 figure
Electron in a magnetic field and two-dimensional point potentials
This paper presents a brief review of the electron properties in two-dimensional systems which contain zero-range scatterers and which are subjected to a magnetic field. The electron spectrum is described for a periodic arrangement of point scatterers and rational magnetic flux per unit cell. Delocalized states on the Landau levels are constructed for the case of positional disorder. The electron localization in a one-dimensional disordered set of scatterers is studied. Application to the study of electron transmission through quantum dots and ballistic channels is reviewed