Dissipation-induced flat bands

Flat bands are an ideal environment to realize unconventional electronic phases. Here, we show that fermionic systems with dissipation governed by a Bloch Lindbladian can dispersionless for sufficiently strong coupling appropriately engineered bath. These flat emerge in "dark space" of the system-environment and long-lived virtue symmetry protection from dissipation. We exhibit robustness this mechanism general one two band models without spin, discuss conditions their experimental realization such as 2D material on superconducting substrate.