141 research outputs found
Equilibrium of anchored interfaces with quenched disordered growth
The roughening behavior of a one-dimensional interface fluctuating under
quenched disorder growth is examined while keeping an anchored boundary. The
latter introduces detailed balance conditions which allows for a thorough
analysis of equilibrium aspects at both macroscopic and microscopic scales. It
is found that the interface roughens linearly with the substrate size only in
the vicinity of special disorder realizations. Otherwise, it remains stiff and
tilted.Comment: 6 pages, 3 postscript figure
Strongly Localized Electrons in a Magnetic Field: Exact Results on Quantum Interference and Magnetoconductance
We study quantum interference effects on the transition strength for strongly
localized electrons hopping on 2D square and 3D cubic lattices in a magnetic
field B. In 2D, we obtain closed-form expressions for the tunneling probability
between two arbitrary sites by exactly summing the corresponding phase factors
of all directed paths connecting them. An analytic expression for the
magnetoconductance, as an explicit function of the magnetic flux, is derived.
In the experimentally important 3D case, we show how the interference patterns
and the small-B behavior of the magnetoconductance vary according to the
orientation of B.Comment: 4 pages, RevTe
Fractal-Mound Growth of Pentacene Thin Films
The growth mechanism of pentacene film formation on SiO2 substrate was
investigated with a combination of atomic force microscopy measurements and
numerical modeling. In addition to the diffusion-limited aggregation (DLA) that
has already been shown to govern the growth of the ordered pentacene thin
films, it is shown here for the first time that the Schwoebel barrier effect
steps in and disrupts the desired epitaxial growth for the subsequent layers,
leading to mound growth. The terraces of the growing mounds have a fractal
dimension of 1.6, indicating a lateral DLA shape. This novel growth morphology
thus combines horizontal DLA-like growth with vertical mound growth.Comment: (5 Figures). Accepted to PR B (in print
Magnetic Properties of the Metamagnet Ising Model in a three-dimensional Lattice in a Random and Uniform Field
By employing the Monte Carlo technique we study the behavior of Metamagnet
Ising Model in a random field. The phase diagram is obtained by using the
algorithm of Glaubr in a cubic lattice of linear size with values ranging
from 16 to 42 and with periodic boundary conditions.Comment: 4 pages, 6 figure
On the Scale-Invariant Distribution of the Diffusion Coefficient for Classical Particles Diffusing in Disordered Media.-
The scaling form of the whole distribution P(D) of the random diffusion
coefficient D(x) in a model of classically diffusing particles is investigated.
The renormalization group approach above the lower critical dimension d=0 is
applied to the distribution P(D) using the n-replica approach. In the annealed
approximation (n=1), the inverse gaussian distribution is found to be the
stable one under rescaling. This identification is made based on symmetry
arguments and subtle relations between this model and that of fluc- tuating
interfaces studied by Wallace and Zia. The renormalization-group flow for the
ratios between consecutive cumulants shows a regime of pure diffusion for small
disorder, in which P(D) goes to delta(D-), and a regime of strong disorder
where the cumulants grow infinitely large and the diffusion process is ill
defined. The boundary between these two regimes is associated with an unstable
fixed-point and a subdiffusive behavior: =Ct**(1-d/2). For the quenched
case (n goes to 0) we find that unphysical operators are generated raisng
doubts on the renormalizability of this model. Implications to other random
systems near their lower critical dimension are discussed.Comment: 21 pages, 1 fig. (not included) Use LaTex twic
Magneto-Conductance Anisotropy and Interference Effects in Variable Range Hopping
We investigate the magneto-conductance (MC) anisotropy in the variable range
hopping regime, caused by quantum interference effects in three dimensions.
When no spin-orbit scattering is included, there is an increase in the
localization length (as in two dimensions), producing a large positive MC. By
contrast, with spin-orbit scattering present, there is no change in the
localization length, and only a small increase in the overall tunneling
amplitude. The numerical data for small magnetic fields , and hopping
lengths , can be collapsed by using scaling variables , and
in the perpendicular and parallel field orientations
respectively. This is in agreement with the flux through a `cigar'--shaped
region with a diffusive transverse dimension proportional to . If a
single hop dominates the conductivity of the sample, this leads to a
characteristic orientational `finger print' for the MC anisotropy. However, we
estimate that many hops contribute to conductivity of typical samples, and thus
averaging over critical hop orientations renders the bulk sample isotropic, as
seen experimentally. Anisotropy appears for thin films, when the length of the
hop is comparable to the thickness. The hops are then restricted to align with
the sample plane, leading to different MC behaviors parallel and perpendicular
to it, even after averaging over many hops. We predict the variations of such
anisotropy with both the hop size and the magnetic field strength. An
orientational bias produced by strong electric fields will also lead to MC
anisotropy.Comment: 24 pages, RevTex, 9 postscript figures uuencoded Submitted to PR
Non-Ergodic Dynamics of the 2D Random-phase Sine-Gordon Model: Applications to Vortex-Glass Arrays and Disordered-Substrate Surfaces
The dynamics of the random-phase sine-Gordon model, which describes 2D
vortex-glass arrays and crystalline surfaces on disordered substrates, is
investigated using the self-consistent Hartree approximation. The
fluctuation-dissipation theorem is violated below the critical temperature T_c
for large time t>t* where t* diverges in the thermodynamic limit. While above
T_c the averaged autocorrelation function diverges as Tln(t), for T<T_c it
approaches a finite value q* proportional to 1/(T_c-T) as q(t) = q* -
c(t/t*)^{-\nu} (for t --> t*) where \nu is a temperature-dependent exponent. On
larger time scales t > t* the dynamics becomes non-ergodic. The static
correlations behave as Tln{x} for T>T_c and for T<T_c when x < \xi* with \xi*
proportional to exp{A/(T_c-T)}. For scales x > \xi*, they behave as (T/m)ln{x}
where m is approximately T/T_c near T_c, in general agreement with the
variational replica-symmetry breaking approach and with recent simulations of
the disordered-substrate surface. For strong- coupling the transition becomes
first-order.Comment: 12 pages in LaTeX, Figures available upon request, NSF-ITP 94-10
Non-perturbative phenomena in the three-dimensional random field Ising model
The systematic approach for the calculations of the non-perturbative
contributions to the free energy in the ferromagnetic phase of the random field
Ising model is developed. It is demonstrated that such contributions appear due
to localized in space instanton-like excitations. It is shown that away from
the critical region such instanton solutions are described by the set of the
mean-field saddle-point equations for the replica vector order parameter, and
these equations can be formally reduced to the only saddle-point equation of
the pure system in dimensions (D-2). In the marginal case, D=3, the
corresponding non-analytic contribution is computed explicitly. Nature of the
phase transition in the three-dimensional random field Ising model is
discussed.Comment: 12 page
Decoherence in Disordered Conductors at Low Temperatures, the effect of Soft Local Excitations
The conduction electrons' dephasing rate, , is expected to
vanish with the temperature. A very intriguing apparent saturation of this
dephasing rate in several systems was recently reported at very low
temperatures. The suggestion that this represents dephasing by zero-point
fluctuations has generated both theoretical and experimental controversies. We
start by proving that the dephasing rate must vanish at the limit,
unless a large ground state degeneracy exists. This thermodynamic proof
includes most systems of relevance and it is valid for any determination of
from {\em linear} transport measurements. In fact, our
experiments demonstrate unequivocally that indeed when strictly linear
transport is used, the apparent low-temperature saturation of is
eliminated. However, the conditions to be in the linear transport regime are
more strict than hitherto expected. Another novel result of the experiments is
that introducing heavy nonmagnetic impurities (gold) in our samples produces,
even in linear transport, a shoulder in the dephasing rate at very low
temperatures. We then show theoretically that low-lying local defects may
produce a relatively large dephasing rate at low temperatures. However, as
expected, this rate in fact vanishes when , in agreement with our
experimental observations.Comment: To appear in the proceedings of the Euresco Conference on Fundamental
Problems of Mesoscopic Physics, Granada, September 2003, Kluwe
Analytical results on quantum interference and magnetoconductance for strongly localized electrons in a magnetic field: Exact summation of forward-scattering paths
We study quantum interference effects on the transition strength for strongly
localized electrons hopping on 2D square and 3D cubic lattices in the presence
of a magnetic field B. These effects arise from the interference between phase
factors associated with different electron paths connecting two distinct sites.
For electrons confined on a square lattice, with and without disorder, we
obtain closed-form expressions for the tunneling probability, which determines
the conductivity, between two arbitrary sites by exactly summing the
corresponding phase factors of all forward-scattering paths connecting them. An
analytic field-dependent expression, valid in any dimension, for the
magnetoconductance (MC) is derived. A positive MC is clearly observed when
turning on the magnetic field. In 2D, when the strength of B reaches a certain
value, which is inversely proportional to twice the hopping length, the MC is
increased by a factor of two compared to that at zero field. We also
investigate transport on the much less-studied and experimentally important 3D
cubic lattice case, where it is shown how the interference patterns and the
small-field behavior of the MC vary according to the orientation of B. The
effect on the low-flux MC due to the randomness of the angles between the
hopping direction and the orientation of B is also examined analytically.Comment: 24 pages, RevTeX, 8 figures include
- …