Minimal Zeeman field requirement for a topological transition in superconductors

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.

arXiv comment8 pages; figure added, clarifications added to main text; submission to SciPost

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Cited by in corpus (6)

• Electronic properties of InAs/EuS/Al hybrid nanowires
• Semiconductor-ferromagnet-superconductor planar heterostructures for 1D topological superconductivity
• Majorana zero modes in gate-defined germanium hole nanowires
• Integrating micromagnets and hybrid nanowires for topological quantum computing
• Topological superconductivity in a magnetic-texture coupled Josephson junction
• Subgap states in semiconductor-superconductor devices for quantum technologies: Andreev qubits and minimal Majorana chains