Quantum phase transitions in strongly disordered topological insulators

Topological phases of matter are usually characterized by the so-called topological invariants, e.g. the Chern number or the Z₂ invariant, that assume translational invariance. Recent studies have shown that topological invariants can be used not only to characterize pristine and/or weakly disordered materials, but also noncrystalline systems such as topological Anderson insulators, amorphous systems, and quasicrystals. For such systems, due to the lack of Bloch periodicity, the topological characterization is done using local makers, like the local Chern number or the Bott index. However, why topological systems are immune to strong disorder and when a disorder-induced topological phase transition occurs are fundamental questions that remain open. This study provides insight on these issues by studying quantum phase transitions in topological Anderson insulators, more specifically, by investigating the criticality and the universality of local markers and the Bott index in a disorder-driven topological quantum phase transition.