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

TL;DR

This paper investigates Majorana bound states in magnetic chains on superconducting honeycomb lattices, revealing phase diagrams, robustness of topological phases, and diverse energy oscillation behaviors influenced by magnetic field and chain length.

Contribution

It provides the first detailed phase diagrams for MBSs in honeycomb systems, highlighting the dependence on spiral angle and magnetic field, and explores the evolution of bound states with system parameters.

Findings

Topological regions are robust even at large Zeeman fields.

Energy oscillations of MBSs vary with magnetic field strength.

Topological phase can depend on chain length, with smooth transition to in-gap states.

Abstract

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 phase diagrams showing the topological regions (where MBSs appear), which are strongly dependent on the spiral angle along the chain of the magnetic moments. In particular, find large regions where the topological phase is robust even at large values of the local Zeeman field, thus producing topological regions without an upper bound. Moreover, we show that the energy oscillations of the MBSs can show very different behavior with magnetic field strength. In some parameter regimes we find increasing oscillations amplitudes and decreasing periods, while in the other regimes the complete opposite behavior is found with increasing magnetic field strength. 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.