Edge-selective extremal damping from topological heritage of dissipative Chern insulators

One of the most important practical hallmarks of topological matter is the presence of topologically protected, exponentially localised edge states at interfaces of regions characterised by unequal topological invariants. Here, we show that even when driven far from their equilibrium ground state, Chern insulators can inherit topological edge features from their parent Hamiltonian. In particular, we show that the asymptotic long-time approach of the non-equilibrium steady state, governed by a Lindblad Master equation, can exhibit edge-selective extremal damping. This phenomenon derives from edge states of non-Hermitian extensions of the parent Chern insulator Hamiltonian. The combination of (non-Hermitian) topology and dissipation hence allows to design topologically robust, spatially localised damping patterns.