many-body methods*

First principles calculations of the second harmonic generation (SHG) of various semiconducting 2D materials including transition metal dichalcogenides (TMDs) are performed using a time-dependent Bethe-Salpeter Equation (TDBSE) nonequilibrium Green’s function approach. It is shown that by increasing simulation time, spectral resolution can be improved, resolving features in the SHG spectrum that can be attributed to excited states of excitons. By comparing the differences in excited exciton energies to the differences observed experimentally, a calibration metric for the degree of over- or under-binding of the excitons can be formulated. Moreover, the degree to which substrate screening in these materials modifies not only the binding energy and the fundamental gap, but also the relative energies of excited states, is explored. The relative intensities of the excited exciton peaks in the SHG are also examined for the additional layer of information they can provide beyond corresponding peaks in the first-order spectra. This focus on a more precise understanding of excitonic resonances in the second harmonic spectrum lays the groundwork for a more systematic use of this TDBSE method for studying nonlinear optical properties in 2D materials.