Chiral damping with persistent edge states: interplay of spectral topology and band topology in open quantum systems

We study the dynamical consequences of combining the non-Hermitian skin effect with topological edge states. Focusing on the paradigmatic dissipative Hofstadter model, we find that the time-dependent particle density exhibits both chiral damping (due to the non-Hermitian skin effect) and edge-selective extremal damping (rooted in persistent topological edge states). We find that the time scales of chiral damping and edge-selective extremal damping decouple due to boundary-induced spectral topology, thus allowing observation of both effects under dynamics. We identify intermediate magnetic fields as the most favorable regime, since chiral damping is then partially recovered. More generally, our work sheds light on how open quantum systems are impacted by the combined presence of spectral and band topologies, and how their interplay can be probed directly.