Marginally localized edges of time-reversal symmetric topological superconductors

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 gapless insulating Majorana edges are generically exponentially localized and trap Majorana zero modes. Interestingly, for a statistically time-reversal symmetric edge (symmetry is broken locally, but the symmetry breaking order parameter is zero on average), 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.

Automated summary

The study demonstrates that the one-dimensional helical Majorana edges of two-dimensional time-reversal symmetric topological superconductors can become gapless and insulating under certain conditions, related to edge velocity and interaction. This gapless insulating edge breaks time-reversal symmetry locally, resembling static mass potentials or dynamic Ising spins. Investigating this phenomenon may lead to a better understanding of the exotic properties of topological superconductors.