Kinetic roughening in surfaces of crystals growing on disordered substrates

Abstract

Substrate disorder effects on the scaling properties of growing crystalline surfaces in solidification or epitaxial deposition processes are investigated. Within the harmonic approach there is a phase transition into a low-temperature (low-noise) superrough phase with a continuously varying dynamic exponent z > 2 and a non-linear response. In the presence of the KPZ nonlinearity the disorder causes the lattice effects to decay on large scales with an intermediate crossover behavior. The mobility of the rough surface has a complex dependence on the temperature and the other physical parameters.

Nonequilibrium dynamics below the super-roughening transition

“…d i = 0, the model exhibits a roughening transition in the same universality class as the Kosterlitz-Thouless transition 9 , at a temperature T r separating a flat phase at low T from a logarithmically (thermally) rough one above T r . The presence of disorder is known to modify significantly the nature of the transition 10,11,12 . The so-called superroughening transition occurs at a temperature T g = T r /2 = 2/π.…”

“…Although these models have been extensively studied, both analytically 16 and numerically 17,18,19 , these works have mainly focused on the equilibrium properties. Among them the static roughness of the interface has been investigated thoroughly and for the dynamics the dynamical exponent z 11,20 . The latter was found to depend continuously on T and computed using the renormalization group (RG) up to one loop in the vicinity of T g , where the fixed point is controlled by the small parameter τ = (T g − T )/T g .…”

Pinning and sliding of tethered monolayers on disordered substrates

“…with ζ a thermal noise, can also be studied by dynamical renormalization group methods [19]. The detailed treatment of this model is described in Appendix C. Regularization of the perturbative expansion of the dynamic response leads to a renormalized friction coefficient γ, from which the dynamic exponent can be extracted …”

Variational study of the random-fieldXYmodel

“…Most theoretical studies of this model have focused on the random-field vortex-free XY case, which is equivalent to the random phase sine-Gordon model. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] Recently, a disorder dependent variational approach has been proposed for this problem [18]. In this approach, the disorder enters only through a unique variable u = d x cos(2πd( x)), where d( x) is a random phase.…”