The coupling between electrons and phonons is central in condensed matter, being at the root of some of the most exotic phases of matter, including superconductivity. It is however often crudely approximated to be a single constant in theories of quantum states of matter, neglecting its momentum dependence which is known to be large and crucial for even a qualitative understanding of quantum phases in real materials. A new phase of matter, named pair density wave, was discovered recently and is fundamentally based on the momentum dependence of the electron-phonon coupling. This internship, aims to study the momentum dependence of the electron-phonon coupling and how it can give birth to new phases of matter, using both ab-initio (DFT or GW) and analytical methods.