Tilting of the magnetic field in Majorana nanowires: critical angle and zero-energy differential conductance

Semiconductor nanowires with strong spin-orbit coupling and proximity-induced s-wave superconductivity in an external magnetic field have been the most promising settings for approaches towards experimental evidence of topological Majorana zero-modes. We investigate the effect of tilting the magnetic field relative to the spin-orbit coupling direction in a simple continuum model and provide an analytical derivation of the critical angle, at which the topological states disappear. We also obtain the differential conductance characteristic of a junction with a normal wire for different tilting angles and propose the qualitative change of the dependence of the zero-energy differential conductance on the tunnel barrier strength at the critical angle as a new criterion for establishing the topological nature of the observed signal.