We investigate the effect of interactions on the stability of a disordered,
two-dimensional topological insulator realized as an array of nanowires or
chains of magnetic atoms on a superconducting substrate. The Majorana
zero-energy modes present at the ends of the wires overlap, forming a
dispersive edge mode with thermal conductance determined by the central charge
c of the low-energy effective field theory of the edge. We show numerically
that, in the presence of disorder, the c=1/2 Majorana edge mode remains
delocalized up to extremely strong attractive interactions, while repulsive
interactions drive a transition to a c=3/2 edge phase localized by disorder.
The absence of localization for strong attractive interactions is explained by
a self-duality symmetry of the statistical ensemble of disorder configurations
and of the edge interactions, originating from translation invariance on the
length scale of the underlying mesoscopic array.Comment: 5+2 pages, 8 figure
