Power laws in surface physics: The deep, the shallow and the useful

TL;DR

This paper explores the prevalence of power law relationships in surface physics, emphasizing the importance of prefactors and critically examining the distinction between trivial and nontrivial power laws through recent experimental and theoretical studies.

Contribution

It provides a critical analysis of power laws in surface physics, highlighting the significance of prefactors and clarifying the nature of trivial versus nontrivial power laws.

Findings

Power laws are common in surface growth and dynamics.

Prefactors carry essential information beyond the power law exponents.

The distinction between trivial and nontrivial power laws is critically examined.

Abstract

The growth and dynamics of solid surfaces displays a multitude of power law relationships, which are often associated with geometric self-similarity. In many cases the mechanisms behind these power laws are comparatively trivial, and require little more than dimensional analysis for their derivation. The information of interest to surface physicists then resides in the prefactors. This point will be illustrated by recent experimental and theoretical work on the growth-induced roughening of thin films and step fluctuations on vicinal surfaces. The conventional distinction between trivial and nontrivial power laws will be critically examined in general, and specifically in the context of persistence of step fluctuations.