  Atom manipulation by scanning tunneling microscopy was used to construct
quantum dots on the InAs(111)A surface. Each dot comprised six ionized indium
adatoms. The positively charged adatoms create a confining potential acting on
surface-state electrons, leading to the emergence of a bound state associated
with the dot. By lining up the dots into N-dot chains with alternating tunnel
coupling between them, quantum-dot molecules were constructed that revealed
electronic boundary states as predicted by the Su-Schrieffer-Heeger (SSH) model
of one-dimensional topological phases. Dot chains with odd N were constructed
such that they host a single end or domain-wall state, allowing one to probe
the localization of the boundary state on a given sublattice by scanning
tunneling spectroscopy. We found probability density also on the forbidden
sublattice together with an asymmetric energy spectrum of the chain-confined
states. This deviation from the SSH model arises because the dots are charged
and create a variation in onsite potential along the chain - which does not
remove the boundary states but shifts their energy away from the midgap
position. Our results demonstrate that topological boundary states can be
created in quantum-dot arrays engineered with atomic-scale precision.
