  Heteroepitaxial structures based on Bi$_{2}$Te$_{3}$-type topological
insulators (TIs) exhibit exotic quantum phenomena. For optimal characterization
of these phenomena, it is desirable to control the interface structure during
film growth on such TIs. In this process, adatom mobility is a key factor. We
demonstrate that Pb mobility on the Bi$_{2}$Te$_{3}$(111) surface can be
modified by the engineering local strain, {\epsilon}, which is induced around
the point-like defects intrinsically forming in the Bi$_{2}$Te$_{3}$(111) thin
film grown on a Si(111)-7 $\times$ 7 substrate. Scanning tunneling microscopy
observations of Pb adatom and cluster distributions and first-principles
density functional theory (DFT) analyses of the adsorption energy and diffusion
barrier E$_{d}$ of Pb adatom on Bi$_{2}$Te$_{3}$(111) surface show a
significant influence of {\epsilon}. Surprisingly, E$_d$ reveals a cusp-like
dependence on {\epsilon} due to a bifurcation in the position of the stable
adsorption site at the critical tensile strain {\epsilon}$_{c}$ $ \approx $
0.8%. This constitutes a very different strain-dependence of diffusivity from
all previous studies focusing on conventional metal or semiconductor surfaces.
Kinetic Monte Carlo simulations of Pb deposition, diffusion, and irreversible
aggregation incorporating the DFT results reveal adatom and cluster
distributions compatible with our experimental observations.
