Two-dimensional spectroscopy of two-dimensional materials: A Mahan-Nozières-De Dominicis model of electron-exciton scattering

In this paper, we provide a systematically convergable and efficient numerical approach to simulate multitime correlation functions in the Mahan-Nozi\`eres-De Dominicis model, which crudely mimics the spectral properties of doped two-dimensional (2D) semiconductors such as monolayer transition metal dichalcogenides. We apply this approach to study the coherent 2D electronic spectra of the model. We show that several experimentally observed phenomena, such as peak asymmetry and coherent oscillations in the waiting-time dependence of the trion-exciton cross peaks of the 2D rephasing spectrum, emerge naturally in our approach. Additional features are also present which find no correspondence with experimentally expected behavior. We trace these features to the infinite hole mass property of the model. We use this understanding to construct an efficient approach which filters out configurations associated with the lack of exciton recoil, enabling the connection to previous work and providing a route to the construction of realistic 2D spectra over a broad doping range in 2D semiconductors.