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We investigate dissipation-induced p-wave paired states of fermions in twodimensions and show the existence of spatially separated Majorana zero modes ina phase with vanishing Chern number. We construct an explicit and natural modelof a dissipative vortex that traps a single of these modes, and establish itstopological origin by mapping the problem to a chiral one-dimensional wirewhere we observe a non-equilibrium topological phase transition characterizedby an abrupt change of a topological invariant (winding number). We show thatthe existence of a single Majorana zero mode in the vortex core is intimatelytied to the dissipative nature of our model. Engineered dissipation opens uppossibilities for experimentally realizing such states with no Hamiltoniancounterpart.

Majorana Modes in Driven-Dissipative Atomic Superfluids With Zero Chern Number