Symmetry reduction and boundary modes for Fe chains on an s-wave superconductor

We investigate the superconducting phases and boundary modes for a quasi-1D system formed by up to three Fe chains on an s-wave superconductor, motivated by a recent experiment. While the Rashba type spin-orbit coupling together with a magnetic ordering is necessary to drive the system to be of nontrivial topology, we show that the onsite [Formula: see text] spin-orbit term, inter-chain diagonal hopping couplings, and magnetic disorders in the Fe chains are crucial in determining the symmetry classes of superconducting phases, which can be topologically trivial or nontrivial in different parameter regimes. In general multiple low-energy Andreev bound states, as well as a single Majorana zero mode if the phase is topological, are obtained in the ends of Fe chains. The nontrivial symmetry reduction mechanism is uncovered to provide an understanding of the present results, and may explain the zero-bias peak observed in the experiment. The present study can be applied to generic multiple-chain system.