First-principles theory of infrared vibrational spectroscopy of metals and semimetals: Application to graphite

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We develop an ab initio method to simulate the infrared vibrational response of metallic systems in the framework of time-dependent density functional perturbation theory. By introducing a generalized frequency-dependent Born effective charge tensor, we show that phonon peaks in the reflectivity of metals can be always described by a Fano function, whose shape is determined by the complex nature of the frequency-dependent effective charges and electronic dielectric tensor. The IR vibrational properties of graphite, chosen as a representative test case to benchmark our method, are found to be accurately reproduced. Our approach offers a first-principle scheme for the prediction and understanding of IR reflectance spectra of metals, that may represent one of the few available tools of investigation of these materials when subjected to extremely high-pressure conditions.