Quantized electrical, thermal, and spin transports of non-Hermitian clean and dirty two-dimensional topological insulators and superconductors

From lattice-regularized models, devoid of any non-Hermitian (NH) skin effects, here we compute the electrical (σxy), thermal (κxy), and spin (σxyˢᵖ) Hall, and the electrical (Gₓₓ) and thermal (Gₓₓᵗʰ) longitudinal conductivities for appropriate NH planar topological insulators and superconductors related to all five nontrivial Altland-Zirbauer symmetry classes in their Hermitian limits. These models feature real eigenvalues over an extended NH parameter regime, only where the associated topological invariants remain quantized. In this regime, the NH quantum anomalous and spin Hall insulators show quantized σxy and Gₓₓ, respectively, the NH $p+ip$ (p±ip) pairing shows half-quantized κxy (Gₓₓᵗʰ), while the NH $d+id$ pairing shows quantized κxy and σxyˢᵖ in the clean and weak disorder (due to random pointlike charge impurities) regimes. We compute these quantities in experimentally realizable suitable six-terminal setups using the Kwant software package. But, in the strong disorder regime, all these topological responses vanish and with the increasing non-Hermiticity in the system this generic phenomenon occurs at weaker disorder.