Structural spillage: an efficient method to screen amorphous topological materials

While topological phases of matter are not restricted to crystals, there is no efficient method for predicting which amorphous solids are topological. In order to enable a high-throughput screening of amorphous topological materials, it is desirable to find a computationally efficient quantity, compatible with first-principle calculations. In this work, we introduce the structural spillage, a quantity that predicts the topological state of an unknown amorphous state by comparing it to a known reference crystal. To illustrate its potential, we benchmark it using tight-binding and first-principles calculations on two-dimensional amorphous bismuth and its bilayer, showing a transition between trivial and topological phases. Our work sets the basis to predict topological amorphous solids efficiently, opening up a large material class where to explore topological phenomena.