Disorder-induced phase transitions in a quasi 1-D Majorana wire

In a strictly 1D spinless p-wave superconductor, disorder is known to induce a phase transition between a topologically nontrivial phase and a trivial insulating phase when the mean free path $l$ becomes of the order of the superconducting coherence length $\xi$. We show that, in constrast, a multichannel spinless p-wave superconductor goes through a series of phase transitions alternating between topologically trivial and nontrivial phases upon increasing the disorder strength. The number of phase transitions equals the channel number $N$ and each phase transition is accompanied by a Dyson singularity in the density of states $\nu(\varepsilon) \propto \varepsilon^{-1}|\ln\varepsilon|^{-3} $. The observed behavior is the result of an effective chiral symmetry allowing us to analytically investigate the phase boundaries and the density of states. The latter displays a power-law singularity $\nu(\varepsilon) \propto \varepsilon^{|\alpha|-1}$ for small energies $\varepsilon$ away from the critical points. Using the concept of ``superuniversality,'' we relate the exponent $\alpha$ to the wire's transport properties at zero energy and, hence, to the mean free path and the superconducting coherence length.