Physical Insights on the Phonon Dispersion of TiS₂

Abstract

Titanium disulfide is a quasi-2D transition-metal dichalcogenide relevant for various potential applications. To exploit its technological capabilities, it is important to determine its fundamental properties including the lattice dynamics. The TiS 2 phonon dispersion curves available to date do not reproduce properly the experimental data for several reasons: i) all available experimental data are not taken into consideration, thus poor theory-experiment agreements have been obtained; ii) the (unknown) frequency of the infrared mode A 2u is erroneously assumed; and iii) such incorrect assignment has propagated in the literature, particularly in phonon dispersion calculations. It is presented here a thorough density functional theory analysis to determine the phonon dispersion curves of TiS 2 , accounting for the frequencies of all experimental phonon data available to date. These include the frequencies of nine zone-edge Raman active modes of Ag-intercalated TiS 2 , in addition to infrared, Raman, and neutron scattering data. An incorrect frequency assignment of the A 2u mode in the literature is thoroughly discussed. Moreover, results of attenuated total reflection terahertz spectroscopy applied to TiS 2 are provided. A self-intercalation paradigm is presented to give a rationale for the temperature dependence of the poorly understood Raman features observed in pristine TiS 2 at frequencies above the A 1g mode.

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

“…Our theoretical model assuming an ideal structure of 1 T -TiS 2 (see Section ) provides a qualitative explanation for the presence of the high-energy shoulder, as typically observed in the high-energy side of the A 1g band, as well as its intensity increase with the temperature. , However, independent spectroscopic and microscopic experiments indicate that realistic TiS 2 samples are nonstoichiometric, and their actual formula is Ti 1+ x S 2 where x is a positive numbertypically in the range of 2–4%. ,,,, The excess titanium appears as additional Ti atoms inside the van der Waals gaps . As interlayer titanium atoms have been one of the most often cited hypotheses of the “shoulder” band’s formation in Raman spectra of TiS 2 , – ,,, the impact of this defect on phonons in TiS 2 deserves separate consideration.…”

“…29 Therefore, further study is needed to fully understand the temperature-induced blue shift of the reported "shoulder" band. 15,16 Recently, 28 an explanation has been proposed which assumes that the thermally-or intercalationinduced enlargement of the interlayer distance might lead to a motion of the Ti i atoms from the high-symmetry (0, 0, 1/2) positions to lower-symmetry positions�located closer to one of the layers. This was expected to stiffen the split A 1g -like phonon modes and increase the "shoulder" band's frequency.…”

“…15,16 The presence of the shoulder has been reported for multiple laser wavelengths in the range of 488−633 nm (1.95−2.54 eV) with similar relative intensities of the A 1g and "Sh" features. [13][14][15][16][17][18][19][20]24 To date, the most often stated hypotheses of the origin of the A 1g band's shoulder involve phonon stiffening due to the presence of excess titanium atoms in the interlayer gaps [14][15][16]20,24,28 and the overtone (or summation) processes. 15,16,18,24 None of them has yet been fully confirmed.…”

Stacking Order-Dependent Electronic, Optical, and Charge Transport Properties of van der Waals GaS/WXY (X/Y = S, Se, Te) Heterostructures

“…Given the weak vdW interaction in the interface, Grimme’s method is employed to simulate the effect of the interlayer vdW force in phonon dispersion calculation. It is worth mentioning that even though some materials have vdW interactions, no trace of them can be found in the experimental data, which may be related to their inherently weak nature . But, compared with the general layered structure, the interface interaction of the Janus-based heterostructure is stronger, which is determined by the intrinsic dipole moment of the Janus monolayer .…”

“…It is worth mentioning that even though some materials have vdW interactions, no trace of them can be found in the experimental data, which may be related to their inherently weak nature. 31 But, compared with the general layered structure, the interface interaction of the Janus-based heterostructure is stronger, which is determined by the intrinsic dipole moment of the Janus monolayer. 32 We present phonon dispersion relations of GaS/SWSe (Figure 1c) and GaS/SeWS (Figure 1d) heterostructures, indicating that the flipping of Janus monolayers has little effect on the vibrational properties of heterostructures.…”