Dissipation Induced Flat Bands in Two Dimensions

Flat bands are an ideal environment to realize strongly-correlated electron systems and to engineer unconventional phases, as their behavior is entirely governed by electronic interactions. Two-dimensional moiré lattices, such as magic-angle twisted bilayer graphene, have recently emerged as a promising route to realize flat bands, however moiré lattices are not the only platform with which to realize flat bands. Here we present a general scenario where flat bands emerge via the introduction of dissipation into systems that have dispersive bands in the zero-dissipation limit. To this end, we develop a Lindbladian approach to study dissipative electronic band structures, which arise from the coupling of a two-dimensional system to a substrate. We reveal a "flat-band condition" on the form of dissipation, under which flat bands with long lifetimes emerge from a broad class of electronic band structures. We analyze ramifications for a paradigmatic model of a Chern insulator, and finally discuss possible experimental signatures of these dissipation-induced flat bands.