Density of states at disorder-induced phase transitions in a multichannel Majorana wire

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 nu(epsilon) proportional to epsilon(-1)vertical bar ln epsilon vertical bar(-3), whereas nu(epsilon) proportional to epsilon(vertical bar alpha vertical bar-1) has a power-law singularity for small energies e 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 a to the wire's transport properties at zero energy and, hence, to the mean free path l and the superconducting coherence length xi.