Edge reconstruction and local topology fluctuations in non-crystalline quantum spin Hall insulators

Quantum spin Hall insulators are materials characterized by an insulating bulk and conductive helical edge states protected by the non-trivial topology of the bulk electronic structure. These are robust against moderate amounts of disorder, until Anderson localization occurs and destroys the topological phase. Remarkably, disorder can also induce a topological phase – known as topological Anderson insulator – starting from an otherwise pristine trivial phase.



In this talk, I will discuss disorder-driven topological phase transition in non-crystalline Kane-Mele models through local topological and quantum-metric markers in large disordered supercells.



First, I will introduce a suite of techniques to calculate $\mathbb{Z}_2$ topological invariants in non-crystalline quantum spin Hall insulators, applicable to both finite and extended systems. Then, I will present numerical simulations unraveling the role of local topology fluctuations and of edge reconstruction in the presence of Anderson disorder and vacancies. Finally, I will discuss the peculiar local properties of topological Anderson insulators in comparison to the conventional disordered quantum spin Hall phase and comment on similarities and differences with vacancy-driven topological phase transitions.