We study the spin waves of the triangular skyrmion crystal that emerges in a two-dimensional spin lattice model as a result of the competition between Heisenberg exchange, Dzyalonshinkii–Moriya interactions, Zeeman coupling and uniaxial anisotropy. The calculated spin wave bands have a finite Berry curvature that, in some cases, leads to non-zero Chern numbers, making this system topologically distinct from conventional magnonic systems. We compute the edge spin-waves, expected from the bulk-boundary correspondence principle, and show that they are chiral, which makes them immune to elastic backscattering. Our results illustrate how topological phases can occur in self-generated emergent superlattices at the mesoscale.The authors would like to thank funding from grants Fondecyt 1150072, ICM P10-061-F by Fondo de Innovación para la Competitividad-MINECON and Anillo ACT 1117. ASN also acknowledges support from Financiamiento Basal para Centros Científicos y Tecnológicos de Excelencia, under Project No. FB 0807(Chile)
