Chiral Bogoliubov excitations in nonlinear bosonic systems

We present a versatile scheme for creating topological Bogoliubov excitations in weakly interacting bosonic systems. Our proposal relies on a background stationary field that consists of a kagome vortex lattice, which breaks time-reversal symmetry and induces a periodic potential for Bogoliubov excitations. In analogy to the Haldane model, no external magnetic field or net flux is required. We construct a generic model based on the two-dimensional nonlinear Schr\"odinger equation and demonstrate the emergence of topological gaps crossed by chiral Bogoliubov edge modes. Our scheme can be realized in a wide variety of physical systems ranging from nonlinear optical systems to exciton-polariton condensates.