Minimal model of charge and pairing density waves in X-ray scattering experiments

Competing density waves play an important role in the mystery of high-temperature cuprate superconductors. In spite of the large amount of experimental evidence, the fundamental question of whether these modulations represent charge or pairing density waves (CDWs or PDWs) is still debated. Here we present a method to answer this question using both momentum and energy-resolved resonant X-ray-scattering maps. Starting from a minimal model of density waves in superconductors, we identify distinctive signatures of incipient CDWs and PDWs. The generality of our approach is confirmed by a self-consistent solution of an extended Hubbard model with attractive interaction. By considering the available experimental data, we claim that the spatial modulations in cuprates have a predominant PDW character. Our work paves the way for using x ray to identify competing and intertwined orders in superconducting materials.