  In this experimental study, we use scanning tunneling microscopy and
spectroscopy to investigate Yu-Shiba-Rusinov states induced by 4f-shell
rare-earth Gd adatoms on a superconducting Nb(110) surface. We engineer Gd atom
chains along the substrate's $[1\overline{1}0]$ and $[001]$ directions,
revealing distinct behaviors in differently oriented chains.
$[1\overline{1}0]$-oriented Gd chains exhibit spectroscopic features at their
ends, identifying them as trivial edge states, while $[001]$-oriented Gd chains
display zero-energy edge states, suggesting non-trivial nature. Notably, Gd
chains with four atoms--independent of their particular orientation--exhibit a
uniform zero-energy mode along the entire chain. These findings call for
further research and a theoretical framework to describe rare-earth-based
structures on superconductors.
