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

Abstract

An NN-channel spinless p-wave superconducting wire is known to go through a series of NN 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(ε)ε1lnε3\nu(\varepsilon) \propto \varepsilon^{-1}|\ln\varepsilon|^{-3} , whereas ν(ε)εα1\nu(\varepsilon) \propto \varepsilon^{|\alpha|-1} has a power-law singularity for small energies ε\varepsilon away from the critical points. Using the concept of "superuniversality" [Gruzberg, Read, and Vishveshwara, Phys. Rev. B 71, 245124 (2005)], we are able to relate the exponent α\alpha to the wire's transport properties at zero energy and, hence, to the mean free path ll and the superconducting coherence length ξ\xi.Comment: 4+1 pages, 3 figure

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