Topological Markers in Disordered, Amorphous, and Quasicrystalline Materials Using KPM.

We implement the kernel polynomial method (KPM) to investigate the topological properties of two and three dimensional materials without translation invariance. By efficiently calculating topological markers, such as the local Chern number and local magnetoelectric coupling, we assess the topological character of disordered model systems. Furthermore, by calculating surface density of states, the ARPES spectra can be simulated for nonperiodic samples. We use these methods to search for material candidates of amorphous and quasicrystalline topological insulators.