Interacting topological phases in Fibonacci quasicrystals*

Recently it was realized that quasicrystals could exhibit non-trivial topological properties and topological equivalence between different types of quasicrystals (such as the Harper model and the Fibonacci quasicrystal). Exciton-polaritons have been recently employed to experimentally verify both band structure and the topological character of the Fibonacci quasicrystal. Given these recent advancements, it is essential to understand the effects of interactions, such as exciton-exciton interactions, on the topological nature of the states corresponding to topological quasicrystals. In this work, we have studied the interacting topological phases in Fibonacci quasicrystals and examined the possible experimental signatures for the effect of interactions in exciton-polariton systems formed in quasicrystal structures.