Topological superconductivity in ferromagnetic atom chains beyond the deep-impurity regime

TL;DR

This paper develops an analytical framework for understanding topological superconductivity in ferromagnetic atom chains on superconductors with Rashba spin-orbit coupling, revealing multiple topological phases and properties of Majorana states.

Contribution

It generalizes the deep-impurity approach to arbitrary subgap energies and introduces a flat-band Hamiltonian to efficiently analyze topological phases.

Findings

Identifies five distinct topological phases.

Shows topological band formation does not require fine-tuning of Shiba energies.

Provides insights into Majorana bound states in the system.

Abstract

Recent developments in the search for topological superconductivity have brought lattices of magnetic adatoms on a superconductor into intense focus. In this work we will study ferromagnetic chains of adatoms on superconducting surfaces with Rashba spin-orbit coupling. Generalising the deep-impurity approach employed extensively in previous works to arbitrary subgap energies, we formulate the theory of the subgap spectrum as a nonlinear matrix eigenvalue problem. We obtain an essentially analytical description of the subgap spectrum, allowing an efficient study of the topological properties. Employing a flat-band Hamiltonian sharing the topological properties of the chain, we evaluate the $\mathbb{Z}$-valued winding number and discover five distinct topological phases. Our results also confirm that the topological band formation does not require the decoupled Shiba energies to be fine-tuned to the gap centre. We also study the properties of Majorana bound states in the system.