Minimal Zeeman field requirement for a topological transition in superconductors

TL;DR

This paper establishes that in superconductors with Zeeman fields, a topological transition necessitates the Zeeman energy to locally surpass the superconducting pairing by at least the full Hamiltonian's energy gap, regardless of system geometry.

Contribution

It derives rigorous bounds on topological transitions in superconductors with Zeeman fields, showing the minimal Zeeman energy needed for topological phases.

Findings

Topological transition requires Zeeman energy to exceed pairing by the energy gap.

Results are independent of system geometry and dimensionality.

Provides fundamental bounds for Majorana quasiparticle platforms.

Abstract

Platforms for creating Majorana quasiparticles rely on superconductivity and breaking of time-reversal symmetry. By studying continuous deformations to known trivial states, we find that the relationship between superconducting pairing and time reversal breaking imposes rigorous bounds on the topology of the system. Applying these bounds to $s$-wave systems with a Zeeman field, we conclude that a topological phase transition requires that the Zeeman energy at least locally exceed the superconducting pairing by the energy gap of the full Hamiltonian. Our results are independent of the geometry and dimensionality of the system.