  Artificial lattices created by assembling atoms on a surface with scanning
tunneling microscopy present a platform to create matter with tailored
electronic, magnetic and topological properties. However, such artificial
lattices studies to date have focused exclusively on surfaces with weak
spin-orbit coupling. Here, we created artificial and coupled quantum dots by
fabricating quantum corrals from iron atoms on the prototypical Rashba surface
alloy, BiCu2, using low-temperature scanning tunneling microscopy. We
quantified the quantum confinement of such quantum dots with various diameter
and related this to the spatially dependent density of states, using scanning
tunneling spectroscopy. We found that the density of states shows complex
distributions beyond the typical isotropic patterns seen in radially symmetric
structures on (111) noble metal surfaces. We related these to the
energy-dependent interplay of the confinement potential with the hexagonal
warping and multiple intra- and interband scattering vectors, which we
simulated with a particle-in-a-box model that considers the Rashba-type band
structure of BiCu2. Based on these results, we studied the effect of coupling
two quantum dots and exploited the resultant anisotropic coupling derived from
the symmetry of the various scattering channels. The large anisotropy and
spin-orbit coupling provided by the BiCu2 platform are two key ingredients
toward creation of correlated artificial lattices with non-trivial topology.
