Quantized electrical and thermal responses of two-dimensional disordered (non-)Hermitian topological insulators and supercondcutors.*

Altland-Zirnbauer topological classification of quantum phases of matter shows that there are five topologically nontrivial classes in every spatial dimension. Particularly in two spatial dimensions, there are two insulating (namely, quantum Hall and quantum spin Hall insulators) and three superconducting (namely, $p+ip$, $d+id$ and $p pm ip$ pairings) AZ phases. The bulk topological invariant of these phases of matter manifests quantized electrical and thermal responses that can be experimentally measured in multi-terminal Hall bar geometries. In this work, I will demonstrate such quantized electric and thermal responses of disordered topological insulators and superconductors, computed within the scattering matrix formalism using the software package Kwant. Furthermore, I will show that in the weak disorder regime such quantized responses are robust, while they vanish smoothly for strong disorder. Finally, I will show that the jurisdiction of these outcomes extends to the landscape of non-Hermitian dirty two-dimensional topological insulators and superconductors.