Topological Diagnosis of Strongly Correlated Electron Systems

The intersection of electronic topology and strong correlations offers a rich platform to discover exotic quantum phases of matter and unusual materials. An overarching challenge that impedes the discovery is how to diagnose strongly correlated electronic topology. Here, we develop a framework to address this outstanding question, and illustrate its power in the setting of electronic topology in Mott insulators. Based on single-particle Green's functions, the concept of a Green's function Berry curvature -- which is frequency dependent -- is introduced. We apply this notion in a system that contains symmetry-protected nodes in its noninteracting bandstructure; strong correlations drive the system into a Mott insulating state, creating contours in frequency-momentum space where the Green's function vanishes. The Green's function Berry flux of such zeros is found to be quantized, and is as such direct probe of the system's topology. Our framework allows for a systematic search of strongly correlated topological materials with Green's function topology.