/* that two dimensional topological insulators are conducting at their edges */
Two-dimensional topological insulators are special category of degenerated topological insulators, their anomalous effects of which apply only at the edge states. These normal ones are conducting by their whole surface. It requires very little to do for to learn it - just the visiting the topological insulator topic at Wikipedia. Once you start argue without even bothering to read this primary source, you're just about to being hit at your self-confidence, so I perceive the public arguing without learning a bit masochistic.
A topological insulator is a material with non-trivial topological order that behaves as an insulator in its interior but whose surface contains conducting states, meaning that electrons can only move along the surface of the material.
Of course, the edges state are even more prone to the expelling of electrons, than the plain surface, so that the edges of topological insulators are usually even more conductive, than the rest of surface. So that when the layer of topological insulator gets scratched, then its conductivity increases, whereas this one of normal conductor will decrease.
/* In the purple bronze superconductor, it is a full functioned superconductor with the Meissner_effect in place but is weak and an unusual one */
Because it's "one-dimensional", as the article title says. The dimensionality is the key for understanding of these materials and their mutual differences. The normal HT superconductors are two-dimensional in similar way, like the normal topological insulators are three-dimensional.
It's worth to note, that the superconductors are sorta opposite type of materials, than the topological insulators: the good topological insulators are only rarely good superconductors and vice-versa. The above material (molybdenum bronze) is exceptional by its ability to serve in both ways, but apparently this ability is compromised just because it must compress the electrons both inside the bulk, both to expel them at the surface at the same moment.
I don't think, that this material will be ever important from practical perspective, because the superconductive paths within 1D superconductors only rarely form a continuum across crystal boundaries, so that these materials aren't good superconductors in common polycrystalline phase.
