Nonlinear dynamics of surface steps

Surface steps are key elements in the dynamics of a crystal surface below its thermodynamic roughening transition, because they constitute long-lived structural defects which are nevertheless highly mobile and prone to strong fluctuations [1]. The description of surface morphology evolution in terms of the thermodynamics and kinetics of steps goes back at least half a century [2]. During the past few decades the subject has experienced a significant revival due to the availability of imaging methods such as scanning tunneling microscopy, which allow for a direct visualization of step conformation and step motion on the nanoscale; see [3–7] for recent reviews. In this chapter I will focus specifically on cases where steps have been found to display complex dynamic behavior, such as oscillatory shape evolution under constant driving. The examples to be discussed below can be naturally organized according to the underlying topology of the step configurations: We first consider driven single-layer islands (closed step loops), and then vicinal surfaces (arrays of parallel steps). A certain familiaritywith the basic thermodynamics and kinetics of crystal surfaces is assumed; for an elementary introduction the reader may consult [8].