Marginally localized edges of time-reversal symmetric topological superconductors

TL;DR

This paper studies how random interactions and velocities can induce a gapless, insulating, and localized phase in the helical Majorana edges of 2D topological superconductors, revealing new topological edge phenomena.

Contribution

It introduces a mechanism for edge localization and gap opening in time-reversal symmetric topological superconductors due to disorder and interactions, with implications for Majorana zero modes.

Findings

Edge states can become gapless and insulating due to disorder and interactions.

Localized Majorana zero modes persist despite absence of ballistic transport.

The low-energy theory maps to a Dyson model with diverging density of states.

Abstract

We demonstrate that the one-dimensional helical Majorana edges of two-dimensional time-reversal symmetric topological superconductors (class DIII) can become gapless and insulating by a combination of random edge velocity and interaction. Such a gapless insulating edge breaks time-reversal symmetry inhomogeneously, and the local symmetry broken regions can be regarded as static mass potentials or dynamical Ising spins. In both limits, we find that such glassy Majorana edges are generically exponentially localized and trap Majorana zero modes. Interestingly, for a statistically time-reversal symmetric edge, the low-energy theory can be mapped to a Dyson model at zero energy, manifesting a diverging density of states and exhibiting marginal localization (i.e., a diverging localization length). Although the ballistic edge state transport is absent, the localized Majorana zero modes reflect the nontrivial topology in the bulk. Experimental signatures are also discussed.