Recent experimental studies have found that magnetic impurities deposited on superconducting monolayer NbSe$_2$ generate coupled Yu-Shiba-Rusinov bound states. Here we consider ferromagnetic chains of impurities which induce a Yu-Shiba-Rusinov band and harbor Majorana bound states at the chain edges. We show that these topological phases are stabilized by strong Ising spin-orbit coupling in the monolayer and examine the conditions under which Majorana phases appear as a function of distance between impurities, impurity spin projection, orientation of chains on the surface of the monolayer, and strength of magnetic exchange energy between impurity and superconductor.
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