Explaining Mysterious “Shoulder” Raman Band in TiS2 by Temperature-dependent Anharmonicity and Defects

In this study, we comprehensively investigate the shape of Raman spectra in titanium disulfide (TiS2) and its temperature dependence, using first-principles calculations and a rigorous theoretical approach to evaluate the corresponding Raman scattering cross sections. Our analysis includes anharmonicity-induced effects: phonon–phonon interactions and the thermal expansion of the 1T-TiS2 crystal. We aim to establish the origin of a not yet fully understood Raman feature often observed at the high-energy side of the band corresponding to the out-of-plane A1g phonon modecommonly called the “shoulder” band. We show that TiS2 is an example of a counterintuitive situation in which a relatively large anharmonicity of the system and its specific two-phonon density of states can lead to a highly asymmetric A1g bandconsisting of the main band and a high-energy shoulder. Although the presence of the “shoulder” band is confirmed for ideal 1T-TiS2 crystals, we also consider realistic TiS2 systems characterized by the often-reported presence of excess interlayer titanium atoms. According to our simulation, such defects lead to the splitting of the A1g phonon mode, resulting in the formation of a high-energy shoulder independent of the anharmonicity-induced mechanism depicted above. The dependence of the phonon splitting on the amount and spatial distribution of the extra titanium atoms is also investigated.