Chiral symmetries and Majorana fermions in coupled magnetic atomic chains on a superconductor

TL;DR

This paper investigates how magnetic structures in coupled atomic chains on superconductors influence topological superconductivity, revealing that chain number and magnetic configuration determine the topological invariants and robustness of Majorana states.

Contribution

It introduces a comprehensive analysis of magnetic phases and topological invariants in coupled atomic chains, highlighting the role of chiral symmetry and chain parity in topological states.

Findings

Topologically nontrivial states can be realized in N-chain triangular ladders.

Noncoplanar states with even N have Z2 invariants, odd N have integer Z invariants.

Chiral symmetry in noncoplanar states is robust against certain disorders.

Abstract

We study the magnetic structures and their connections with topological superconductivity due to proximity effect for coupled magnetic atomic chains deposited on a superconductor. Several magnetic phases are self-consistently determined, including both the coplanar and non-coplanar ones. For a $N$-chain triangular atomic ladder, topologically nontrivial superconducting states can always be realized, but strongly depend on its magnetic structure and the number of atomic chains. When $N$ is even, the topologically nontrivial states with noncoplanar structures are characterized by $\mathbb{Z}_{2}$ invariants, while the topologically nontrivial noncoplanar states with an odd $N$ are characterized by integer $\mathbb{Z}$ invariants, due to the presence of a new chiral symmetry. The new chiral symmetry for the noncoplanar states is found to be robust against the on-site disorder, as long as the crystal reflection symmetry is respected.