What is a topological defect?

Question

I tried reading [the Wikipedia page](https://en.m.wikipedia.org/wiki/Topological_defect) but that confused me even more.

In: Physics

Answer 1

I think the most generic way to describe it is:

You have *a thing*. Then you have some sort of unwanted or unexpected feature in that thing that *just won’t go away no matter how much you want it to*.

Like trying to make a flat sheet of paper fit over a curved surface always resulting in a crease, there’s just some sort of mismatch that keeps persisting because there’s no way to “cancel it out”.

Or the problem of “brushing a sphere”, where if you have hair on a sphere (like a human head), there’s no way to brush it flat and there’s always going to be a swirl somewhere.

I’m not familiar with solitons in waves and stuff, but I am familiar with the other example, defects in crystal structures.

And that’s basically the same thing. The crystal structure is meant to be perfectly repeatable into infinity, but the real world is messy. So you have mismatches. An extra layer, or a missing one. Something shifted in the wrong way. And it results in a feature (the dislocation) that, if you try to “smooth it out”, will just move about, because there’s no way to rearrange the atoms to make it just disappear. 

The only way to get rid of them is if there’s another dislocation that’s “opposite” to it, and they cancel out when they meet, or they reach the surface and just end up creating a surface flaw there.