Boundary spin polarization as robust signature of topological phase transition in Majorana nanowires

We show that the boundary charge and spin can be used as alternative signatures of the topological phase transition in topological models such as semiconducting nanowires with strong Rashba spin-orbit interaction in the presence of a magnetic field and in proximity to an $s$-wave superconductor. We identify signatures of the topological phase transition that do not rely on the presence of Majorana zero-energy modes and, thus, can serve as independent probes of topological properties. The boundary spin component along the magnetic field, obtained by summing contributions from all states below the Fermi level, has a pronounced peak at the topological phase transition point. Generally, such signatures can be observed at boundaries between topological and trivial sections in nanowires and are stable against disorder.