Universality issues in surface kinetic roughening of thin solid films

Since publication of the main contributions on the theory of kinetic roughening more than fifteen years ago, many works have been reported on surface growth or erosion that employ the framework of dynamic scaling. This interest was mainly due to the predicted existence of just a few universality classes to describe the statistical properties of the morphology of growing surfaces and interfaces that appear in a wide range of physical systems. Nowadays, this prediction seems to be inaccurate. This situation has caused a clear detriment of these studies in spite of the undeniable existence of kinetic roughening in many different real systems, and without a clear understanding of the reasons behind the mismatch between theoretical expectations and experimental observations. In this chapter we aim to explore existing problems and shortcomings of both the theoretical and experimental approaches, focusing mainly on growth of thin solid films. Our analysis suggests that the theoretical framework as yet is not complete, while more systematic and consistent experiments need to be performed. Once these issues are taken into account, a more consistent and useful theory of kinetic roughening might develop.Comment: Review article to appear in ``Advances in Condensed Matter and Statistical Mechanics", ed. E. Korutcheva and R. Cuerno. To be published by Nova Science Publishers. 22 pages. 4 eps figure

Quantum symmetries in the free field realization of Wn algebras

7 pages, no figures.-- MSC2000 codes: Primary: 81R50; Secondary: 17B37, 17B81, 81R10.MR#: MR1140143 (92m:81106)$W_n$ algebras are considered in their free field representation to show that they are endowed with a quantum group symmetry which is a $Z_2$ twist à la Drinfel'd of $U_{q+}({\rm sl}(n))\times U_{q-}({\rm sl}(n))$. We use the contour picture of quantum groups due to Gómez and Sierra. A sample computation for the $R$ matrix is also performed.R.C. was supported by a FPI grant by the Spanish MEC.Publicad

Nanoscale pattern formation: an interplay between hard and soft condensed matter physics

[Abstract of]: Nanopatterning2017: 9th International Workshop on Nanoscale Pattern Formation at Surfaces ; FOR3NANO: Formation of 3D Nanostructures by Ion Beams, 26-30 June 2017, Helsinki, FinlandThis talk will attempt a brief overview on the interplay between hard and soft condensed matter physics with respect to the formation of nanoscale-sized patterns..

Dynamic effects induced by renormalization in anisotropic pattern forming systems

The dynamics of patterns in large two-dimensional domains remains a challenge in non-equilibrium phenomena. Often it is addressed through mild extensions of one-dimensional equations. We show that full 2D generalizations of the latter can lead to unexpected dynamical behavior. As an example we consider the anisotropic Kuramoto-Sivashinsky equation, that is a generic model of anisotropic pattern forming systems and has been derived in different instances of thin film dynamics. A rotation of a ripple pattern by $90^{\circ}$ occurs in the system evolution when nonlinearities are strongly suppressed along one direction. This effect originates in non-linear parameter renormalization at different rates in the two system dimensions, showing a dynamical interplay between scale invariance and wavelength selection. Potential experimental realizations of this phenomenon are identified.Comment: 5 pages, 3 figures; supplemental material available at journal web page and/or on reques

Short-range stationary patterns and long-range disorder in an evolution equation for one-dimensional interfaces

A novel local evolution equation for one-dimensional interfaces is derived in the context of erosion by ion beam sputtering. We present numerical simulations of this equation which show interrupted coarsening in which an ordered cell pattern develops with constant wavelength and amplitude at intermediate distances, while the profile is disordered and rough at larger distances. Moreover, for a wide range of parameters the lateral extent of ordered domains ranges up to tens of cells. This behavior is new in the context of dynamics of surfaces or interfaces with morphological instabilities. We also provide analytical estimates for the stationary pattern wavelength and mean growth velocity

Variational mean-field study of a continuum model of crystalline tensionless surfaces

9 pages, 6 figures.-- PACS nrs.: 64.60.Ht, 64.60.Cn, 68.35.Rh, 81.10.Aj.-- ArXiv pre-print available at: http://arxiv.org/abs/cond-mat/9912013We study analytically the equilibrium and near-equilibrium properties of a model of a d-dimensional surface relaxing via linear surface diffusion and subject to a lattice potential. We employ the variational mean-field formalism introduced by Saito for the study of the sine-Gordon model. In equilibrium, our variational theory predicts a first-order roughening transition between a flat low-temperature phase and a rough high-temperature phase with the properties of the linear molecular-beam epitaxy equation. Moreover, the study of a Gaussian approximation to the Langevin dynamics of the system indicates that the surface shows hysteresis when temperature is continuously tuned. Out of equilibrium, these approximate Langevin dynamics show that the surface mobility can have different behaviors as a function of a driving flux. Some considerations are made regarding different underlying lattices, and connections are drawn to related models or different approaches to the same model we study.This work was partially supported by DGES Grant Nos. PB96-0119 and HB1999-0018, and EPSRC Grant No. GR/M04426.Publicad