Pressure-induced electronic and isostructural phase transitions in PdPS: Raman, x-ray, and first-principles study

Application of pressure is known to be an effective tool for tuning structural and electronic properties of transition metal dichalcogenides. In this work we present evolution of PdPS with pressure using Raman spectroscopy and synchrotron x-ray diffraction up to 26 GPa, complemented with first-principles theoretical analysis of PdPS under pressure up to 36 GPa. Raman spectra reveal changes in the pressure derivatives of Raman frequencies at $P\sim 2$, 11, and 21 GPa, suggesting three isostructural electronic phase transitions in PdPS. The pressure-dependent x-ray diffraction shows a sudden rise in the bulk modulus from $90\pm 3$ to $123\pm 7$ GPa occurring at $P\sim 11$ GPa. Using first-principles density functional theory calculations, we demonstrate that the low-pressure phase transitions are associated with changes in direct band gap at $\mathrm{\Gamma }$ point while the high-pressure (at $P=21$ GPa) transition is associated with semiconductor to semimetal transition. From analysis of PdPS at higher pressures, we predict a structural phase transition in PdPS at $P\sim 32$ GPa from orthorhombic to monoclinic structure.

Figure 1

Crystal structure of PdPS with (a) conventional unit cell, (b) top and (c) side views of its monolayer, and (d) Brillouin zone (BZ) of bulk PdPS.

Figure 2

(a) Pressure-dependent evolution of Raman spectra of PdPS from 0 to 26 GPa. Solid green lines are fits to individual peaks and solid red lines are a sum of all peaks fit to the experimental data. (b) Eigenvectors of all its the Raman active modes obtained from theoretical calculations of the orthorhombic structure. Note that Pd, P, and S atoms are shown by gray, blue, and yellow color spheres. (c) Schematic diagram showing phase transitions with pressure. Note that we have marked theoretical pressure by $P_c^T$. Abbreviations used SC: semiconductor, M: metal, o: orthorhombic phase, and m: monoclinic phase.

Figure 3

Dependence of phonon frequencies on pressure. Solid red lines linear fits to the experimental data, and dashed vertical blue lines at 2, 11, and 21 GPa indicate the transition pressures, at which the pressure coefficient of some of the modes changes.

Figure 4

(a) XRD patterns of PdPS as a function of pressure. The peak marked with $★$ is due to the gasket. (b) Profile matching in Jana 2006, in which the peak is masked. The solid red line is fit to the experimental data (black circles), and the bottom blue line is the difference between the experimental data and fitted data. Small vertical lines in between are the XRD peaks allowed by symmetry, (c) pressure dependence of volume. Solid red lines are fit using Birch-Murnaghan equation of state [Eq. (1)], and the inset shows pressure dependence of $c/a$.

Figure 5

Calculated frequencies of phonons of bulk PdPS as a function of pressure. Solid lines are linear fits to the data. The pressure coefficients $S=\frac{\delta \omega }{\delta P}({\mathrm{cm}}^{-1}$/GPa) are specified near the lines. Vertical dashed lines indicate pressures at which $S$ changes.

Figure 6

(a) $c/a$ ratio of PdPS as a function of pressure and (b) calculated pressure dependence of crystal cell volume of PdPS. Vertical dashed lines indicate the transition pressure. Solid red lines in (b) are fits to Birch-Murnaghan equation of state on the two sides of the dashed line. (c) Electronic structure of PdPS at $P\sim 0$ GPa, exhibiting direct band gap of 1.02 eV and an indirect band gap 0.80 eV marked by arrows. (d) Variation in the indirect and direct band gap between states at $\mathrm{\Gamma }$ to a point in the vicinity of $R$ point along the $R\text{−}T$ path. Electronic structure of the orthorhombic phase of PdPS at $P\sim 24$ GPa (e) and $P\sim 30$ GPa (f). Note that VBM shifts to a wave vector midway along the $\mathrm{\Gamma }\text{−}X$ path in (e) and (f), whereas CBM remain at the same point as shown in (c). Note that $R^{\prime }$ is marked by dashed line in (c), and VBM and CBM is marked with purple color circles in (e) and (f).

Figure 7

Phonon dispersion of orthorhombic PdPS along the $\mathrm{\Gamma }\text{−}Z$ direction at (a) $P\sim 30$ GPa and (b) $P\sim 32$ GPa. Phonon dispersion of the orthorhombic structure at $P=32$ GPa exhibits an instability, showing that it is unstable at $P>30$ GPa. (c) $B_{1g}$ Raman mode frequency as a function of pressure, which becomes unstable beyond $P\sim 30$ GPa as shown in red squares.