  In a recent article, Huda et al. demonstrated tuneable topological domain
wall states in the c(2$\times$2) chlorinated Cu(100). Their system allows to
experimentally tune the domain wall states using atom manipulation by the tip
of a scanning tunneling microscope (STM). They have realized topological domain
wall states of two prototypical 1D models such as trimer and coupled dimer
chains. However, they did not distinguish trivial domain wall states from
topological ones in their models. As a result, all states of a specific domain
wall are not topological but trivial. Here, we show why the specific domain
wall states are trivial and how to make them topological. This topological
consideration would provide more clear insight on future studies on topological
domain wall states in artificial atomic chains.
