Minimal Zeeman field requirement for a topological transition in superconductors
Kim Pöyhönen (TU Delft - QuTech Advanced Research Centre, TU Delft - QRD/Wimmer Group, Kavli institute of nanoscience Delft)
Daniel Varjas (TU Delft - QuTech Advanced Research Centre, Kavli institute of nanoscience Delft, Stockholm University, TU Delft - QRD/Kouwenhoven Lab)
M.T. Wimmer (TU Delft - QuTech Advanced Research Centre, Kavli institute of nanoscience Delft, TU Delft - QN/Wimmer Group)
Anton Akhmerov (TU Delft - QuTech Advanced Research Centre, TU Delft - QN/Akhmerov Group)
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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.
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