Majorana bound states in magnetic impurity chains: effects of $d$-wave pairing

Abstract

We consider an atomic chain of magnetic impurities on the surface of a spin-orbit coupled superconductor with a dominating $d$-wave and sub-dominating $s$-wave order parameters. In particular, we investigate the properties of the Majorana bound states (MBSs) emerging at the chain end points in the topological phase and how MBSs are affected by the $d$-wave order parameter. We provide a comprehensive picture by both studying time-reversal invariant and breaking superconducting substrates as well as chains oriented in different directions relative to the $d$-wave rotation. We show that increasing the $d$-wave order parameter significantly enhances the localization of MBSs and their protective mini-gap, as long as the direction along which the impurity chain is oriented does not cross any nodal lines of the gap function. Moreover, we find an extra gap-closing for a specific condensate and chain orientation within the topological phase, which we are able to attribute to simple geometrical effects in the corresponding two-dimensional limit. These results show how high-temperature $d$-wave superconductors can be used to significantly enhance the properties and stability of MBSs.

arXiv comment11 pages, 11 figures

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• Supercurrent detection of topologically trivial zero-energy states in nanowire junctions
• Majorana bound state localization and energy oscillations for magnetic impurity chains on conventional superconductors
• High-Temperature Majorana Fermions in Magnet-Superconductor Hybrid Systems
• Robust topological superconductivity in weakly coupled nanowire-superconductor hybrid structures
• Tailoring phase transition from topological superconductor to trivial superconductor induced by magnetic textures of a spin-chain on a $p$-wave superconductor
• Yu-Shiba-Rusinov States and Ordering of Magnetic Impurities Near the Boundary of a Superconducting Nanowire
• Detrimental effects of disorder in two-dimensional time-reversal invariant topological superconductors
• Majorana bound states in d-wave superconductor planar Josephson junction