An N-channel spinless p-wave superconducting wire is known to go through a series of N topological phase transitions upon increasing the disorder strength. Here, we show that at each of those transitions the density of states shows a Dyson singularity ν(ɛ)∝ɛ−1∣∣lnɛ∣∣−3, whereas ν(ɛ)∝ɛ|α|−1 has a power-law singularity for small energies ɛ away from the critical points. Using the concept of “superuniversality” [Gruzberg et al., Phys. Rev. B 71, 245124 (2005)], we are able to relate the exponent α to the wire's transport properties at zero energy and, hence, to the mean free path l and the superconducting coherence length ξ.
