Infrared Peak-Splitting from phonon localization in Solid Hydrogen

We show that the isotope effect leads to a completely different spectroscopic signal in hydrogen-deuterium mixtures, compared to pure elements that have the same crystal structure. This is particularly true for molecular vibrations, which are the main source of information about the structure of high-pressure hydrogen. Mass disorder breaks translational symmetry, meaning that vibrations are localized almost to single molecules, and are not zone-center phonons. In mixtures, each observable IR peak corresponds to a collection of many such molecular vibrations, which have a distribution of frequencies depending on local environment. Furthermore discrete groups of environments cause the peaks to split. We illustrate this issue by considering the IR spectrum of the high pressure Phase III structure of hydrogen, recently interpreted as showing novel phases in isotopic mixtures. We calculate the IR spectrum of hydrogen/deuterium mixtures in the $C2/c$ and $Cmca$-12 structures, showing that isotopic disorder gives rise to mode localization of the high frequency vibrons. The local coordination of the molecules leads to discrete IR peaks. The spread of frequencies is strongly enhanced with pressure, such that more peaks become resolvable at higher pressures, in agreement with the recent measurements.