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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.
We demonstrate that a combination of disorder and interactions in a two-dimensional bulk topological insulator can generically drive its helical edge insulating. We establish this within the framework of helical Luttinger liquid theory and exact Emer
We study the surface of a three-dimensional spin chiral $mathrm{Z}_2$ topological insulator (class CII), demonstrating the possibility of its localization. This arises through an interplay of interaction and statistically-symmetric disorder, that con
The symmetries associated with discrete-time quantum walks (DTQWs) and the flexibilities in controlling their dynamical parameters allow to create a large number of topological phases. An interface in position space, which separates two regions with
The boundary of a topological insulator (TI) hosts an anomaly restricting its possible phases: e.g. 3D strong and weak TIs maintain surface conductivity at any disorder if symmetry is preserved on-average, at least when electron interactions on the s
We study the behavior of spinless fermions in superconducting state, in which the phases of the superconducting order parameter depend on the direction of the link. We find that the energy of the superconductor depends on the phase differences of the