637 research outputs found
Metal-insulator transition in three dimensional Anderson model: universal scaling of higher Lyapunov exponents
Numerical studies of the Anderson transition are based on the finite-size
scaling analysis of the smallest positive Lyapunov exponent. We prove
numerically that the same scaling holds also for higher Lyapunov exponents.
This scaling supports the hypothesis of the one-parameter scaling of the
conductance distribution. From the collected numerical data for quasi one
dimensional systems up to the system size 24 x 24 x infinity we found the
critical disorder 16.50 < Wc < 16.53 and the critical exponent 1.50 < \nu <
1.54. Finite-size effects and the role of irrelevant scaling parameters are
discussed.Comment: 4 pages, 2 figure
Quantum Hall effects in layered disordered superconductors
Layered singlet paired superconductors with disorder and broken time reversal
symmetry are studied. The phase diagram demonstrates charge-spin separation in
transport. In terms of the average intergrain transmission and the interlayer
tunnelling we find quantum Hall phases with spin Hall coefficients of 0 and 2
separated by a spin metal phase. We identify a spin metal-insulator
localization exponent as well as a spin conductivity exponent of ~0.9. In
presence of a Zeeman term an additional phase with spin Hall coefficient of 1
appears.Comment: 4 pages, 4 figure
A matrix ensemble with a preferential basis and its application to disordered metals and insulators
URL: http://www-spht.cea.fr/articles/s93/085The standard ensembles of the random matrix theory are invariant under change of basis. For non interacting electrons in disordered systems, this invariance is broken and deviations from the random matrix theory predictions occur, especially for strong disorder. We consider a generalization of the standard ensembles which includes a preferential basis and which gives rise to a ``screening'' of the logarithmic pairwise interaction between energy levels. In the unitary case, we recover a mathematically tractable distribution of energy levels first introduced by Gaudin. This simplified model provides a qualitative description of level statistics in the metal, insulator and at the mobility edge, which only depends on the dimensionless conductance
--Oscillations for Correlated Electron Pairs in Disordered Mesoscopic Rings
The full spectrum of two interacting electrons in a disordered mesoscopic
one--dimensional ring threaded by a magnetic flux is calculated numerically.
For ring sizes far exceeding the one--particle localization length we
find several --periodic states whose eigenfunctions exhibit a pairing
effect. This represents the first direct observation of interaction--assisted
coherent pair propagation, the pair being delocalized on the scale of the whole
ring.Comment: 4 pages, uuencoded PostScript, containing 5 figures
Failure of single-parameter scaling of wave functions in Anderson localization
We show how to use properties of the vectors which are iterated in the
transfer-matrix approach to Anderson localization, in order to generate the
statistical distribution of electronic wavefunction amplitudes at arbitary
distances from the origin of disordered systems. For
our approach is shown to reproduce exact diagonalization results
available in the literature. In , where strips of width sites
were used, attempted fits of gaussian (log-normal) forms to the wavefunction
amplitude distributions result in effective localization lengths growing with
distance, contrary to the prediction from single-parameter scaling theory. We
also show that the distributions possess a negative skewness , which is
invariant under the usual histogram-collapse rescaling, and whose absolute
value increases with distance. We find for the
range of parameters used in our study, .Comment: RevTeX 4, 6 pages, 4 eps figures. Phys. Rev. B (final version, to be
published
Role of a parallel magnetic field in two dimensional disordered clusters containing a few correlated electrons
An ensemble of 2d disordered clusters with a few electrons is studied as a
function of the Coulomb energy to kinetic energy ratio r_s. Between the Fermi
system (small r_s) and the Wigner molecule (large r_s), an interaction induced
delocalization of the ground state takes place which is suppressed when the
spins are aligned by a parallel magnetic field. Our results confirm the
existence of an intermediate regime where the Wigner antiferromagnetism
defavors the Stoner ferromagnetism and where the enhancement of the Lande g
factor observed in dilute electron systems is reproduced.Comment: 4 pages, 3 figure
Length-dependent oscillations of the conductance through atomic chains: The importance of electronic correlations
We calculate the conductance of atomic chains as a function of their length.
Using the Density Matrix Renormalization Group algorithm for a many-body model
which takes into account electron-electron interactions and the shape of the
contacts between the chain and the leads, we show that length-dependent
oscillations of the conductance whose period depends on the electron density in
the chain can result from electron-electron scattering alone. The amplitude of
these oscillations can increase with the length of the chain, in contrast to
the result from approaches which neglect the interactions.Comment: 7 pages, 4 figure
Localization of non-interacting electrons in thin layered disordered systems
Localization of electronic states in disordered thin layered systems with b
layers is studied within the Anderson model of localization using the
transfer-matrix method and finite-size scaling of the inverse of the smallest
Lyapunov exponent. The results support the one-parameter scaling hypothesis for
disorder strengths W studied and b=1,...,6. The obtained results for the
localization length are in good agreement with both the analytical results of
the self-consistent theory of localization and the numerical scaling studies of
the two-dimensional Anderson model. The localization length near the band
center grows exponentially with b for fixed W but no
localization-delocalization transition takes place.Comment: 6 pages, 5 figure
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
Universal amplitude of the free energy density in finite-size scaling: the Potts universality
Using the numerical results of the finite-size scaling study of the q-state
Potts model by Bloete and Nightingale, we obtain conjectured expressions for
the universal amplitude of the free energy density.Comment: Old paper, for archiving. 4 pages, IOP macr
- …