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 realize dispersionless bands for sufficiently strong coupling to an appropriately engineered bath. These flat bands emerge in a ``dark space'' of the system-environment coupling and are long-lived by virtue of symmetry protection from dissipation. We exhibit the robustness of this mechanism for general one- and two-band models with and without spin, and discuss conditions for their experimental realization such as in a two-dimensional material on a superconducting substrate.