Classification and Prediction of Topological Insulators by Using the Density of States

In order to characterize topological insulators it is customary to use representations of the electronic structure, such as the band structure, where the energy of electrons is represented as a function of their momenta. Topological insulators are then represented as those systems whose surface states have an odd number of crossings at the Fermi level, or, equivalently, as those systems where the spin and momentum is locked at the surface. The density of states, however, cannot in principle be used to distinguish if a material is a topological insulator because it integrates the momentum information for a given energy. In this article, we show that, despite that fact, the density of states of topological insulators show some distinctive characteristics that may even be used to predict if a certain material is of that type or not by using such quantity. We use a series of machine learning algorithms to classify first the density of states and predict then systems with similar densities of states that can lead to new topological materials. We find that, contrary to what would be expected, the densities of states of topological insulators have distinct features that allow to classify and identify these materials according to them. In particular, the DOS of topological insulators tends to exhibit sharper and more concentrated spectral features near the band edges, indicating a narrower distribution of bulk electronic states (spectral localization) rather than spatial localization of surface modes.