Symmetry Reduction and Boundary Modes for Fe-Chains on an s-wave Superconductor

TL;DR

This paper explores the topological phases and boundary modes in Fe-chain superconductors on an s-wave substrate, revealing how spin-orbit coupling, hopping, and disorder influence Majorana and Andreev states, with implications for recent experiments.

Contribution

It uncovers a symmetry reduction mechanism affecting topological phases and clarifies the conditions under which Majorana zero modes may appear in Fe-chain systems.

Findings

Topological and trivial superconducting phases depend on system parameters.

Majorana zero modes are present in the topological regime at chain ends.

Zero-bias peaks in experiments may not always indicate Majorana modes.

Abstract

We investigate the superconducting phase diagram and boundary modes for a quasi-1D system formed by three Fe-Chains on an s-wave superconductor, motivated by the recent Princeton experiment. The $\vec l\cdot\vec s$ onsite spin-orbit term, inter-chain diagonal hopping couplings, and magnetic disorders in the Fe-chains are shown to be crucial for the superconducting phases, which can be topologically trivial or nontrivial in different parameter regimes. For the topological regime a single Majorana and multiple Andreew bound modes are obtained in the ends of the chain, while for the trivial phase only low-energy Andreev bound states survive. Nontrivial symmetry reduction mechanism induced by the $\vec l\cdot\vec s$ term, diagonal hopping couplings, and magnetic disorder is uncovered to interpret the present results. Our study also implies that the zero-bias peak observed in the recent experiment may or may not reflect the Majorana zero modes in the end of the Fe-chains.