645 research outputs found
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.
Boundary hopping and the mobility edge in the Anderson model in three dimensions
It is shown, using high-precision numerical simulations, that the mobility
edge of the 3d Anderson model depends on the boundary hopping term t in the
infinite size limit. The critical exponent is independent of it. The
renormalized localization length at the critical point is also found to depend
on t but not on the distribution of on-site energies for box and Lorentzian
distributions. Implications of results for the description of the transition in
terms of a local order-parameter are discussed
Weak disorder expansion for localization lengths of quasi-1D systems
A perturbative formula for the lowest Lyapunov exponent of an Anderson model on a strip is presented. It is expressed in terms of an energy-dependent doubly stochastic matrix, the size of which is proportional to the strip width. This matrix and the resulting perturbative expression for the Lyapunov exponent are evaluated numerically. Dependence on energy, strip width and disorder strength are thoroughly compared with the results obtained by the standard transfer matrix method. Good agreement is found for all energies in the band of the free operator and this even for quite large values of the disorder strength
Localizations in coupled electronic chains
We studied effects of random potentials and roles of electron-electron
interactions in the gapless phase of coupled Hubbard chains, using a
renormalization group technique. For non-interacting electrons, we obtained the
localization length proportional to the number of chains, as already shown in
the other approaches. For interacting electrons, the localization length is
longer for stronger interactions, that is, the interactions counteract the
random potentials. Accordingly, the localization length is not a simple linear
function of the number of chains. This interaction effect is strongest when
there is only a single chain. We also calculate the effects of interactions and
random potentials on charge stiffness.Comment: no figure, to appear in Phys. Rev.
Strongly correlated wave functions for artificial atoms and molecules
A method for constructing semianalytical strongly correlated wave functions
for single and molecular quantum dots is presented. It employs a two-step
approach of symmetry breaking at the Hartree-Fock level and of subsequent
restoration of total spin and angular momentum symmetries via Projection
Techniques. Illustrative applications are presented for the case of a
two-electron helium-like single quantum dot and a hydrogen-like quantum dot
molecule.Comment: 9 pages. Revtex with 2 GIF and 1 EPS figures. Published version with
extensive clarifications. A version of the manuscript with high quality
figures incorporated in the text is available at
http://calcite.physics.gatech.edu/~costas/qdhelproj.html For related papers,
see http://www.prism.gatech.edu/~ph274c
Conductance Correlations Near Integer Quantum Hall Transitions
In a disordered mesoscopic system, the typical spacing between the peaks and
the valleys of the conductance as a function of Fermi energy is called
the conductance energy correlation range . Under the ergodic hypothesis,
the latter is determined by the half-width of the ensemble averaged conductance
correlation function: . In
ordinary diffusive metals, , where is the diffusion constant
and is the linear dimension of the phase-coherent sample. However, near a
quantum phase transition driven by the location of the Fermi energy , the
above picture breaks down. As an example of the latter, we study, for the first
time, the conductance correlations near the integer quantum Hall transitions of
which is a critical coupling constant. We point out that the behavior of
is determined by the interplay between the static and the dynamic
properties of the critical phenomena.Comment: 4 pages, 4 figures, minor corrections, to appear in Phys. Rev. Let
Effects of Scale-Free Disorder on the Anderson Metal-Insulator Transition
We investigate the three-dimensional Anderson model of localization via a
modified transfer-matrix method in the presence of scale-free diagonal disorder
characterized by a disorder correlation function decaying asymptotically
as . We study the dependence of the localization-length exponent
on the correlation-strength exponent . % For fixed disorder ,
there is a critical , such that for ,
and for , remains that of the
uncorrelated system in accordance with the extended Harris criterion. At the
band center, is independent of but equal to that of the
uncorrelated system. The physical mechanisms leading to this different behavior
are discussed.Comment: submitted to Phys. Rev. Let
The Anderson Transition in Two-Dimensional Systems with Spin-Orbit Coupling
We report a numerical investigation of the Anderson transition in
two-dimensional systems with spin-orbit coupling. An accurate estimate of the
critical exponent for the divergence of the localization length in this
universality class has to our knowledge not been reported in the literature.
Here we analyse the SU(2) model. We find that for this model corrections to
scaling due to irrelevant scaling variables may be neglected permitting an
accurate estimate of the exponent
Electronic transport in strongly anisotropic disordered systems: model for the random matrix theory with non-integer beta
We study numerically an electronic transport in strongly anisotropic weakly
disorderd two-dimensional systems. We find that the conductance distribution is
gaussian but the conductance fluctuations increase when anisotropy becomes
stronger. We interpret this result by random matrix theory with non-integer
symmetry parameter beta, in accordance with recent theoretical work of
K.A.Muttalib and J.R.Klauder [Phys.Rev.Lett. 82 (1999) 4272]. Analysis of the
statistics of transport paramateres supports this hypothesis.Comment: 8 pages, 7 *.eps figure
Multifractality of the quantum Hall wave functions in higher Landau levels
To probe the universality class of the quantum Hall system at the
metal-insulator critical point, the multifractality of the wave function
is studied for higher Landau levels, , for various range of
random potential. We have found that, while the multifractal spectrum
(and consequently the fractal dimension) does vary with , the
parabolic form for indicative of a log-normal distribution of
persists in higher Landau levels. If we relate the multifractality with
the scaling of localization via the conformal theory, an asymptotic recovery of
the single-parameter scaling with increasing is seen, in agreement
with Huckestein's irrelevant scaling field argument.Comment: 10 pages, revtex, 5 figures available on request from
[email protected]
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