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 $L$ 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 $B$, and hopping lengths $t$, can be collapsed by using scaling variables $B_\perp t^{3/2}$, and $B_\parallel t$ 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 $\sqrt{t}$. 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

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

Decoherence in Disordered Conductors at Low Temperatures, the effect of Soft Local Excitations

The conduction electrons' dephasing rate, $\tau_{\phi}^{-1}$, 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 $T\to 0$ limit, unless a large ground state degeneracy exists. This thermodynamic proof includes most systems of relevance and it is valid for any determination of $\tau_{\phi}$ 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 $\tau_{\phi}$ 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 $T \to 0$, 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