Born effective charges and vibrational spectra in super and bad conducting metals

Interactions mediated by electron-phonon coupling are responsible for important cooperative phenomena in metals such as superconductivity and charge-density waves. The same interaction mechanisms produce strong collision rates in the normal phase of correlated metals, causing sizeable reductions of the dc conductivity and reflectivity. As a consequence, low-energy excitations like phonons, which are crucial for materials characterization, become visible in optical infrared spectra. A quantitative assessment of vibrational resonances requires the evaluation of dynamical Born effective charges, which quantify the coupling between macroscopic electric fields and lattice deformations. We show that the Born effective charges of metals crucially depend on the collision regime of conducting electrons. In particular, we describe, within a first principles framework, the impact of electron scattering on the infrared vibrational resonances, from the undamped, collisionless regime to the overdamped, collision-dominated limit. Our approach enables the interpretation of vibrational reflectance measurements of both super and bad conducting metals, as we illustrate for the case of strongly electron-phonon coupled superhydride H$_3$S.