Toward Realistic Amorphous Topological Insulators

The topological properties of materials are, until now, associated with the features of their crystalline structure, although translational symmetry is not an explicit requirement of the topological phases. Recent studies of hopping models on random lattices have demonstrated that amorphous model systems show a nontrivial topology. Using {\it ab initio} calculations we show that two-dimensional amorphous materials can also display topological insulator properties. More specifically, we present a realistic state-of-the-art study of the electronic and transport properties of amorphous bismuthene systems, showing that these materials are topological insulators. These systems are characterized by the topological index $\mathbb{Z}_{2}=1$ and bulk-edge duality, and their linear conductance is quantized, ${\cal G}=2e^{2}/h$, for Fermi energies within the topological gap. Our study opens the path to the experimental and theoretical investigation of amorphous topological insulator materials.