Facet Formation in the Negative Quenched Kardar-Parisi-Zhang Equation

TL;DR

This paper investigates how substrate tilt affects the first-order pinning-depinning transition in the negative quenched KPZ equation, revealing facet formation and transition behavior depending on tilt magnitude.

Contribution

It introduces a detailed analysis of substrate-tilt effects on the PD transition in the negative QKPZ equation, highlighting the role of facet formation and pinning mechanisms.

Findings

Pinned surfaces form a facet with a characteristic slope at the transition.

Transition behavior depends on substrate-tilt: discontinuous for small tilt, continuous for larger tilt.

Critical driving force varies with substrate-tilt, influenced by localized pinning centers.

Abstract

The quenched Kardar-Parisi-Zhang (QKPZ) equation with negative non-linear term shows a first order pinning-depinning (PD) transition as the driving force $F$ is varied. We study the substrate-tilt dependence of the dynamic transition properties in 1+1 dimensions. At the PD transition, the pinned surfaces form a facet with a characteristic slope $s_c$ as long as the substrate-tilt $m$ is less than $s_c$. When $m<s_c$, the transition is discontinuous and the critical value of the driving force $F_c(m)$ is independent of $m$, while the transition is continuous and $F_c(m)$ increases with $m$ when $m>s_c$. We explain these features from a pinning mechanism involving a localized pinning center and the self-organized facet formation.