Tailoring phase transition from topological superconductor to trivial superconductor induced by magnetic textures of a spin-chain on a $p$-wave superconductor

TL;DR

This paper explores how magnetic textures in a spin-chain on a $p$-wave superconductor induce a phase transition to a trivial superconductor, destroying Majorana modes through effective $s$-wave pairing and Shiba band interactions.

Contribution

It provides a combined analytical and numerical study of magnetic impurity-induced phase transitions from topological to trivial superconductivity in $p$-wave systems.

Findings

Magnetic impurity chains can induce an $s$-wave like pairing in $p$-wave superconductors.

The topological phase transition is characterized by gap closing and winding number analysis.

Oscillatory behavior of Shiba bands evidences the formation of effective $s$-wave pairing.

Abstract

We theoretically investigate the phase transition from a non-trivial topological $p$-wave superconductor to a trivial $s$-wave like superconducting phase through a gapless phase, driven by different magnetic textures as an one-dimensional spin-chain impurity, e.g. Bloch-type, in-plane and out-of-plane N\'eel-type spin-chains etc. In our proposal, the chain of magnetic impurities is placed on a spin-triplet $p$-wave superconductor where we obtain numerically as well as analytically an effective $s$-wave like pairing due to spin rotation, resulting in gradual destruction of the Majorana zero modes present in the topological superconducting phase. In particular, when the impurity spins are antiferromagnetically aligned i.e. spiral wave vector $G_{s}=\pi$, the system becomes an effective $s$-wave superconductor without Majorana zero modes in the local density of states. The Shiba bands, on the other hand, formed due to the overlapping of Yu-Shiba-Rusinov states play a crucial role in this topological to trivial superconductor phase transition, confirmed by the sign change in the minigap within the Shiba bands. We also characterize this topological phase transition via gap closing and winding number analysis. Moreover, interference of the Shiba bands exhibiting oscillatory behavior within the superconducting gap, $-\Delta_{p}$ to $\Delta_{p}$, as a function of $G_{s}$, also reflects an important evidence for the formation of an effective $s$-wave pairing. Such oscillation is absent in the $p$-wave regime.