Interacting virtual topological phases in defect-rich two-dimensional materials

We investigate the robustness of virtual topological states---topological phases away from the Fermi energy---against the electron-electron interaction and band filling. As a case study, we employ a realistic model to investigate the properties of vacancy-driven topological phases in transition metal dichalcogenides (TMDs) and establish a connection between the degree of localization of topological wave functions, the vacancy density, and the electron-electron interaction strength with the topological phase robustness. We demonstrate that electron-electron interactions play a crucial role in degrading topological phases thereby determining the validity of single-particle approximations for topological insulator phases. Our findings can be naturally extended to virtual topological phases of a wide range of materials.