Ab initio method for vibrational spectroscopy in conductive systems

Cooperative phenomena in solid-state physics have gained significant attention due to their scientific and technological importance. This relevance was officially acknowledged in the Ginzburg Nobel Lecture in 2004, which emphasized the pursuit of high-temperature superconductivity as a key challenge for the 21st century. Recent technological advancements have enabled a more profound exploration of these phenomena, gathering instances where electronic cooperation is mediated by phonon interactions. However, this research faces experimental challenges that hinder sample characterization. Vibrational spectroscopy plays a key role in sample characterization, especially infrared reflectivity measurement in case of high-pressure environment where the diamond-anvil-cell apparatus is required. However, until recent years, the theoretical description of this experimental technique was confined to insulating systems. Up to now, there is no formulation describing the vibrational contribution to the susceptibility in the damped regime, where scattering effect are non-negligible. This unconventional scenario occurs in systems showing cooperative phenomena mediated by the phonon interaction, since the same interaction at the origin of the cooperative phenomenon also provides a potent scattering mechanism. This thesis proposes a theoretical approach and computational methods to calculate the vibrational response in metals, extending the present formulation to the time domain and damped regime. We apply this method to MgB2 and two super-Hydrides: H3 S and LaH10 where the strong electron-phonon coupling is considered the origin of their exceptional high critical temperature as conventional BCS superconductors.