Amorphous solids are not as random! In our new work we studied, with Q. Marsal and @danielvarjas how to describe topological phases in amorphous lattices! Check this and the paper on the arxiv: https://arxiv.org/abs/2003.13701 

So, solids are made by atoms. A gazillion of them. Many scientists usually like them better when they are nice an ordered in a periodic structure we call a crystal. They are nice clean and symmetric so we can apply nice mathematical theorems to study them.

Now, most of things around you are not nice in this sense. Most of the materials you see are not in their crystalline form, but rather in some amorphous or disordered version. So, are these outside nice theorems and mathematics?

The GOD of disorder was Phil Anderson, @NobelPrize who passed away last Sunday at 96 (still going to the office a few weeks ago!). From him we learned, among many things, that disorder can be studied, and can have beautiful mathematical structures.

In this work we follow this spirit, but now the disorder is in the lattice that forms the solid. The atoms are arranged aperiodially, but not random!

Amorphous solids actually have some order. The atoms in them see an environment that is actually quite similar to their crystal counterparts. It is only at long length scales (the whole material) where we can see that something is different compared to a crystal!

So, what we did in this paper was to use this ‘short range order’ to find phases with beautiful mathematical structure, topological phase, that are typically associated to crystals, this time in amorphous solids!

We are not the first to study amorphous Topological phases but we found a way to use this hidden order to predict when they appear. We think it can eventually open a way to classify them, something that is quite challenging compared to the beautiful symmetric crystals.

I have discussed topological phases in the past. They could be useful for a bunch of technological progress, mostly because of their robustness, even to a completely disordered lattice like in our case. Basically: Nice new material property + topology = robust technology (maybe)

So, now is time to push this to its full potential! Amorphous materials are everywhere, so let’s make topology be everywhere too!