Classification of engineered topological superconductors

TL;DR

This paper provides a comprehensive classification of topological superconductors in various dimensions, revealing new platforms for Majorana fermions and implications for topological quantum computing.

Contribution

It introduces a complete classification scheme for topological superconductors considering inhomogeneous spin-orbit coupling, magnetism, and symmetries, including hidden symmetries affecting topological properties.

Findings

Majorana fermions can emerge without magnetism in certain quasi-1d systems.

Hidden symmetries influence the topological classification of superconductors.

Alternative platforms for topological quantum computing are proposed.

Abstract

I perform a complete classification of 2d, quasi-1d and 1d topological superconductors which originate from the suitable combination of inhomogeneous Rashba spin-orbit coupling, magnetism and superconductivity. My analysis reveals alternative types of topological superconducting platforms for which Majorana fermions are accessible. Specifically, I observe that for quasi-1d systems with Rashba spin-orbit coupling and time-reversal violating superconductivity, as for instance due to a finite Josephson current flow, Majorana fermions can emerge even in the absence of magnetism. Furthermore, for the classification I also consider situations where additional "hidden" symmetries emerge, with a significant impact on the topological properties of the system. The latter, generally originate from a combination of space group and complex conjugation operations that separately do not leave the Hamiltonian invariant. Finally, I suggest alternative directions in topological quantum computing for systems with additional unitary symmetries.