First-principles resonant Raman spectroscopy for 2D materials

We implement first-principles method for resonant Raman spectroscopy of solids based on a second-order Feynman diagram and the Franck-Condon principle. The Raman Intensity is calculated using an expression in the form of the Kramers-Heisenberg-Dirac (KHD) formula. Sum over all phonon configurations is performed using the Fourier transform into the time domain and evaluated with the help of Feynman path integrals. The triple integration method offers a simple and fast numerical approach that accounts for all multiple phonon processes. The ground state and excited state phonon modes are calculated to provide frequencies and equilibrium atomic positions. The computed Raman intensities for MoS2/WS2 heterostructure is in agreement with experimental data. We also explore the resonance properties of the Raman spectrum, in particular its strong dependence on the energy of incident laser and on temperature.