Tomography of zero-energy end modes in topological superconducting wires

We characterize the Majorana zero modes in topological hybrid superconductor-semiconductor wires with spin-orbit coupling and magnetic field, in terms of generalized Bloch coordinates $φ, θ, δ$, and analyze their transformation under SU(2) rotations. We show that, when the spin-orbit coupling and the magnetic field are perpendicular, $φ$ and $δ$ are universal in an appropriate coordinate system. We use these geometric properties to explain the behavior of the Josephson current in junctions of two wires with different orientations of the magnetic field and/or the spin-orbit coupling. We show how to extract from there, the angle $θ$, hence providing a full description of the Majorana modes.

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