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A general expression is introduced for the tracer diffusivity in complexperiodic energy landscapes with more than one distinct hop rate in two- andthree-dimensional diluted systems (low coverage, single-tracer limit). Fordiffusion in two dimensions, a number of formulas are presented for complexcombinations of hop rates in systems with triangular, rectangular and squaresymmetry. The formulas provide values in excellent agreement with Kinetic MonteCarlo simulations, concluding that the diffusion coefficient can be directlydetermined from the proposed expressions without performing such simulations.Based on the diffusion barriers obtained from first principles calculations anda physically-meaningful estimate of the attempt frequencies, the proposedformulas are used to analyze the diffusion of Cu, Ag and Rb adatoms on thesurface and within the van der Waals (vdW) gap of a model topologicalinsulator, Bi$_{2}$Se$_{3}$. Considering the possibility for adsorbateintercalation from the terraces to the vdW gaps at morphological steps, weinfer that, at low coverage and room temperature: (i) a majority of the Rbatoms bounce back at the steps and remain on the terraces, (ii) Cu atoms mostlyintercalate into the vdW gap, the remaining fraction staying at the steps, and(iii) Ag atoms essentially accumulate at the steps and gradually intercalateinto the vdW gap. These conclusions are in good qualitative agreement withprevious experiments.

Low coverage surface diffusion in complex energy landscapes: Analytical solution and application to intercalation in topological insulators