Electronic Band Structure and Optical Properties of HgPS3 Crystal and Layers

Transition metal thiophosphates (MPS3) are of great interest due to their layered structure and magnetic properties. Although HgPS3 may not exhibit magnetic properties, its uniqueness lies in its triclinic crystal structure and in the substantial mass of mercury, rendering it a compelling subject for exploration in terms of fundamental properties. In this work, we present comprehensive experimental and theoretical studies of the electronic band structure and optical properties for the HgPS3 crystal and mechanically exfoliated layers from a solid crystal. Based on absorption, reflectance and photoluminescence measurements supported by theoretical calculations, it is shown that the HgPS3 crystal has an indirect gap of 2.68 eV at room temperature. The direct gap is identified at the Γ point of the Brillouin zone (BZ) ≈ 50 meV above the indirect gap. The optical transition at the Γ point is forbidden due to selection rules, but the oscillator strength near the Γ point increases rapidly and therefore the direct optical transitions are visible in the reflectance spectra approximately at 60–120 meV above the absorption edge, across the temperature range of 40 to 300 K. The indirect nature of the bandgap and the selection rules for Γ point contribute to the absence of near-bandgap emission in HgPS3. Consequently, the photoluminescence spectrum is primarily governed by defect-related emission. The electronic band structure of HgPS3 undergoes significant changes when the crystal thickness is reduced to tri- and bilayers, resulting in a direct bandgap. Interestingly, in the monolayer regime, the fundamental transition is again indirect. The layered structure of the HgPS3 crystal was confirmed by scanning electron microscopy (SEM) and by mechanical exfoliation.

Exfoliation of HgP S 3 Figure S6a shows how nearly transparent a monolayer is when the microscope is on reflection mode and with its diaphragm open.In the case of few-layers (e.g. 1, 2, 3 layers) one expects very low optical contrast, in such a way that the color of the flakes will be very similar to that of the substrate.One way to assure that the flake is a monolayer is by collecting differential reflectance spectrum between the flake and the substrate (Figure S6b) and check the spectral positions of the A, B and C excitons, which are well established for M oS 2 as well as M oSe 2 , W S 2 and W Se 2 .In the case of monolayer M oS 2 the narrow A exciton is located expected at approximately 1.92 eV, while B is at around 2.03 and the broad C exciton is expected at around 2.81 eV, and these values can vary 10-15 meV from flake to flake [1].The flake indicated by the arrow is therefore a monolayer.

Raman Spectroscopy
To the best of our knowledge, there is no literature regarding the Raman modes of HgP S 3 .Therefore, in this study we present an analysis of its vibrational modes by combining experimental data and DFT calculations.Figure S7a shows Raman spectra of bulk HgP S 3 from 10 to 300 K, and 12 peaks can be identified at low temperature, labeled P1 to P12 from low to high frequency, respectively and indicated by the arrows.In general, all of them undergo a slight shift to lower frequencies as the temperature increases (Figure S7b), apart from the usual decrease in intensity.Nevertheless, 7 out of the 12 peaks are still visible at 300 K. P2, P5, P11 and P12 vanish at around 200 K, while P7 vanishes at 280 K, as shows Figure S7b.Peak frequencies were extracted by Lorentz fits.No peak splitting is observed.These results suggest that the compound does not undergo structural phase transition in this temperature range.Raman spectra of exfoliated crystals of HgP S 3 are presented in Figure S7c.Three flakes were investigated at room temperature, and seven peaks can be observed: P1, P3, P4, P6, P8, P9, and P10, in excellent agreement with the spectrum of the bulk crystal at the same temperature.No significant difference between bulk and exfoliated HgP S 3 phonon modes was noticed.The exfoliated flakes were transferred onto a Si/SiO 2 substrate, and the intense peak at around 515 cm −1 is due to the substrate.Phonon calculations at the Γ point of the Brillouin Zone yielded 27 modes, with irreducible representation Γ = 15A g + 12A u , labeled Ag1 to Ag15 and Au1 to Au12, and marked by black and red vertical lines, respectively, in Figure S8.The main feature is at ≈ 241 cm −1 with a corresponding calculated phonon mode at ≈ 244 cm −1 .According to [2], only A g modes are Raman-active.The corresponding calculated phonon frequencies are given in Table S1, together with the frequencies of the 12 peaks experimentally observed at 10 K.The fact that 12 peaks were observed experimentally might be related to the setup configuration: some peaks might only be visible with parallel scattering configuration (the conventional one, used by us, in which incident and scattered light are parallel to each other), while others might only be accessed in cross-scattering configuration.
Figure S8: Raman spectrum of HgP S 3 at 10 K (blue) and 300 K (green), along with calculated phonon modes A g (black) and A u (red).

Figure
Figure S5: FT-IR spectrum of HgP S 3 .

Figure
Figure S6: a) Optical images of mechanically exfoliated M oS 2 flakes transferred to SiO 2 /Si substrate with 20x magnification.Red arrow indicates a monolayer candidate.b) Differential reflectance from the flake indicated by the arrow, which confirms that it is a monolayer.Dashed lines highlight spectral position of excitons A, B, and C. Inset shows an image of the monolayer with 50x magnification and closed diaphragm for better visualization.Red lines indicate the approximate flake dimensions: 27x17x15 µm.

Figure
Figure S7: a) Raman spectra of bulk HgP S 3 from 10 to 300 K. Spectra has been shifted vertically for better visualization.b) Temperature dependence of the frequency of the 12 peaks marked in a) by arrows.c) Raman spectra of exfoliated HgP S 3 flakes at 300 K. Peaks are labelled according to a).

Figure
FigureS10ashows the energy difference of the valence (3 bands) and conduction (2 bands) bands closest to the energy gap.The blue circles indicate the four lowest energy direct transitions at high symmetry points or local minima that have nonzero transition oscillator strengths (See FigureS10b, which presents specific values of these quantities for the x, y and z polarization components).S10c collects information from the previous figures.The size of the circle indicates the sum of the strength components of the transition oscillators, and the colors indicate the transition between specific bands.Higher energy optical transitions are possible at the Γ point, approximately at a few hundreds meV above the absorption edge.

Figure
Figure S10: a) Lowest energy direct transitions with non-zero matrix elements.b) Oscillator strength of each of the transitions for the x, y and z polarization components.c) combines a) and b): size of the circle indicates the sum of the oscillator strength, and the colors indicate the transition between specific bands.

Figure S11 :
Figure S11: Single particle dielectric function of HgP S 3 obtained by density-functional perturbation theory (DFPT).The inset includes a close-up of the edge with arrows marking the band gap, and the lowest optical transitions with non-zero oscillator strength presented in Figure S10a.

Table S1 :
Calculated phonon modes, the 12 experimentally observed peaks from bulk HgP S 3 at 10 K and corresponding frequencies.