Today there exists a strong research focus on topological effects in condensed matter. Initial studies were only focused on non-interacting electronic systems, but attention is now shifting towards the influence of electron-electron interactions and also the broken symmetry states they can generate. Real-world materials bring disorder as a third important component, as many symmetry broken states are sensitive to disorder. Hence, to understand many materials we need to keep a combined focus on topology, electronic correlations, and disorder. Copper oxide high-temperature superconductors (cuprates) with pair breaking edges host a flat band of topological zero-energy states, making them an ideal playground where strong correlations, topology, and disorder are strongly intertwined. In the talk, I will discuss the three way interplay in cuprates which generates a new phase of matter: a fully gapped "phase crystal" state that breaks both translational and time reversal invariance, characterized by a modulation of the d-wave superconducting phase co-existing with a modulating extended s-wave superconducting order. In contrast to conventional wisdom, this phase crystal state is remarkably robust to omnipresent disorder, but only in the presence of strong correlations, thus giving a clear route to its experimental realization . I will also discuss how a combined importance of correlations and topology emerges in a spin-orbit coupled material in proximity to a van Hove singularity .
 D. Chakraborty, T. Löfwander, M. Fogelström & A. M. Black-Schaffer, npj Quantum Materials 7, 44 (2022).
 P. M. Bonetti*, D. Chakraborty*, X. Wu, A. P. Schnyder, arXiv:2304.07100 (2023). *=equal contribution