Edge dark states of dissipative dynamics in topological insulators

The study of topological phases in non-Hermitian systems has become a key area in condensed matter physics, providing a deep understanding of open quantum systems with dissipation. In this work, we study edge dark states (EDSs) in dissipative topologically nontrivial insulators, i.e., the dissipative Haldane model and the dissipative Kane-Mele model on a honeycomb lattice. By deriving a non-Hermitian damping matrix X from the Lindblad master equation, we characterize the system's dissipative dynamics through its Liouvillian spectrum. Numerical calculations demonstrate that EDSs, marked by vanishing imaginary parts in the spectrum (im(\lambda)=0), emerge as topologically protected modes localized at the system's edges. These states remain robust even in the presence of nonzero Hamiltonian contributions, contrary to previous studies showing that such protection required purely dissipative systems. We introduce a double damping matrix \tildeX =diag(X,X^\ast ) to further demonstrate the stability of EDSs against perturbations. This work highlights the interplay between non-Hermitian topology and dissipative dynamics, paving the way for exploring novel dissipative topological phenomena.