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

• Published in: arXiv.org
• Main Authors: Maria-Theresa Rieder, Brouwer, Piet W
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 08.09.2014
• Subjects: Coherence length; Critical point; Density of states; Phase transitions; Physics - Mesoscale and Nanoscale Physics; Superconductivity; Transport properties; Wire
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.1409.1877

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 \(\nu(\varepsilon) \propto \varepsilon^{-1}|\ln\varepsilon|^{-3} \), whereas \(\nu(\varepsilon) \propto \varepsilon^{|\alpha|-1}\) has a power-law singularity for small energies \(\varepsilon\) 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 \(\alpha\) to the wire's transport properties at zero energy and, hence, to the mean free path \(l\) and the superconducting coherence length \(\xi\).