Signature of a topological phase transition in long SN junctions in the spin-polarized density of states

We investigate the spin texture of Andreev bound states and Majorana states in long SN junctions. We show that measuring the spin-polarized density of states (SPDOS) allows one to identify the topological transition. In particular, we find that its total component parallel to the wire is non-zero in the topological phase for the lowest-energy state, while vanishing in the trivial one. Also, the component parallel to the Zeeman field is symmetric between positive and negative energies in the topological phase and asymmetric in the trivial phase. Moreover the SPDOS exhibits a moderate accumulation close to the SN boundary which changes sign when crossing the topological transition. We propose that these signatures may allow one to unambiguously test the formation of a topological phase via spin-resolved transport and STM measurements.