Tomography of Zero-Energy End Modes in Topological Superconducting Wires

Abstract

We describe 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 . When the spin-orbit coupling and the magnetic field are perpendicular, φ and δ are universal in an appropriate coordinate system. We show how to extract the angle θ from the behavior of the Josephson current-phase relation, which enables tomography of the Majorana modes. Simple analytical expressions describe accurately the numerical results.