Computation of topological phase diagram of amorphous Bi_xSb_1-x 2d alloys using artificial neural networks

The entanglement spectrum of a solid is known to contain information regarding the topological behaviour of the material. On the other hand, the Wilson loop is the standard technique to assess if a material is topological or not, provided that it is gapped. For supercells this approach quickly becomes unpractical, or even unusable if the gap disappears, which is why we turn to the entanglement spectrum for the study of disordered systems. In a previous work, we showed that it is possible to train an artificial neural network to identify the topological invariant of disodered systems, using the entanglement spectrum.

We now apply this methodology to a realistic model of 2d bismuth-antimony alloys. Instead of modelling the alloy with the virtual crystal approximation, we use a Slater-Koster description of the bonds to allow for statistical variance. Training a neural network appropriately, we are able to identify the critical concentrations for different allotropes of the crystalline alloy. As we amorphize the solid, we show that even when the localized states close the gap, there are still topological states present in the amorphous phase.