Gap oscillations and Majorana bound states in magnetic chains on superconducting honeycomb lattices

Magnetic chains on superconducting systems have emerged as a platform for realization of Majorana bound states (MBSs) in condensed-matter systems with possible applications to topological quantum computation. In this work, we study the MBSs formed in magnetic chains on two-dimensional honeycomb materials with induced superconductivity. We establish chemical potential vs Zeeman splitting phase diagrams showing that the topological regions (where MBSs appear) are strongly dependent on the spiral angle along the magnetic chain. In some of those regions, the topological phase is robust even for large values of the local Zeeman field, thus producing topological regions which are, in a sense, "unbounded" in the large-field limit. Moreover, we show that the energy oscillations with magnetic field strength due to MBS splitting can show very different behaviors depending on the parameters. In some regimes, we find oscillations with increasing amplitudes and decreasing periods, while in the other regimes the complete opposite behavior is found. We also find that the topological phase can become dependent on the chain length, particularly in topological regions with a very high or no upper bound. In these systems, we see a very smooth evolution from MBSs localized at chain end points to in-gap Andreev bound states spread over the full chain.