  A general expression is introduced for the tracer diffusivity in complex
periodic energy landscapes with more than one distinct hop rate in two- and
three-dimensional diluted systems (low coverage, single-tracer limit). For
diffusion in two dimensions, a number of formulas are presented for complex
combinations of hop rates in systems with triangular, rectangular and square
symmetry. The formulas provide values in excellent agreement with Kinetic Monte
Carlo simulations, concluding that the diffusion coefficient can be directly
determined from the proposed expressions without performing such simulations.
Based on the diffusion barriers obtained from first principles calculations and
a physically-meaningful estimate of the attempt frequencies, the proposed
formulas are used to analyze the diffusion of Cu, Ag and Rb adatoms on the
surface and within the van der Waals (vdW) gap of a model topological
insulator, Bi$_{2}$Se$_{3}$. Considering the possibility for adsorbate
intercalation from the terraces to the vdW gaps at morphological steps, we
infer that, at low coverage and room temperature: (i) a majority of the Rb
atoms bounce back at the steps and remain on the terraces, (ii) Cu atoms mostly
intercalate into the vdW gap, the remaining fraction staying at the steps, and
(iii) Ag atoms essentially accumulate at the steps and gradually intercalate
into the vdW gap. These conclusions are in good qualitative agreement with
previous experiments.
