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

Abstract

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 $\nu (\epsilon )\propto {\epsilon }^{-1}|\ln \epsilon {|}^{-3}$, whereas $\nu (\epsilon )\propto {\epsilon }^{|\alpha |-1}$ has a power-law singularity for small energies $\epsilon$ 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 $\xi$.

4+1 pages, 3 figures

References in corpus (8)

• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Anderson Transitions
• Topological Anderson Insulator
• Topological Anderson Insulator in Three Dimensions
• Localization in disordered superconducting wires with broken spin-rotation symmetry
• Quantum Hall Effect of Massless Dirac Fermions in a Vanishing Magnetic Field
• Thermal metal-insulator transition in a helical topological superconductor

Cited by in corpus (3)

• Anderson localization and the topology of classifying spaces
• Wave-packet spreading in the disordered and nonlinear Su-Schrieffer-Heeger chain
• Topological phases in the presence of disorder and longer-range couplings