Chemical ordering and pressure-induced isostructural and electronic transitions in MoSSe crystal

Isostructural transitions in layered $M{X}_2$ compounds are governed by competing van der Waals (vdW) and Coulomb interactions. While an isostructural transition (at $P\sim$ 20 GPa) has been observed before metallization in ${\mathrm{MoS}}_2$ when subjected to pressure, it is surprisingly missing in layered ${\mathrm{MoSe}}_2$ and ${\mathrm{MoTe}}_2$. Using synchrotron x-ray diffraction and Raman spectroscopic measurements of structural and vibrational properties of layered MoSSe crystals subjected to pressures up to 30 GPa and first-principles density functional theoretical analysis, we demonstrate a layer sliding isostructural transition from its $2H_c^{\prime }$ structure (space group ${P6}_{3}mc$) to a mixed-phase of $2H_a^{\prime }+2H_c^{\prime }$ at $P\sim$ 10.8 GPa, marked by discontinuity in lattice parameters, pressure coefficients of Raman modes, and accompanying changes in electronic structure. The origin of the unusually lower transition pressure of MoSSe compared with ${\mathrm{MoS}}_2$ is shown to be linked to chemical ordering of S and Se atoms on the anionic sublattice, possible because of moderate lattice mismatch between the parent compounds ${\mathrm{MoS}}_2$ and ${\mathrm{MoSe}}_2$ and large interlayer space in the vdW-bonded structure. Notably, we also report a lower-pressure transition observed at $P\sim 3$ GPa and not reported earlier in the isostructural Mo-based chalcogenides, marked by a discontinuity in the pressure coefficient of the $c/a$ ratio and indirect band gap. The transition observed at $P\sim 10.8$ GPa appears due to the change in the sign of the pressure coefficient of the direct band gap originating from inversion of the lowest-energy conduction bands. Our theoretical analysis shows that the phase transition at $P\sim 18$ GPa marked by sharp changes in pressure coefficients of $A_1$ Raman modes is associated with the metallization of the $2H_a^{\prime }$ phase.

Figure 1

(a)–(c) XRD patterns at a few elevated pressures; here, a linear scale is shown for intensity ($y$ axis). Rietveld analysis was used to match the patterns to the ${P6}_{3}mc$ (No. 186) crystal structure at 0.7 GPa with the gsas ii software package [43]. Here, circles and solid lines represent experimental data and calculated patterns, respectively. The lower curve in dark green is the weighted difference between the observed and calculated patterns. The weighted profile $R_{wp}$ factors are shown. The inset in (a) shows the stacking of atoms in the unit cell. (d) Schematic of phase transitions in MoSSe with pressure.

Figure 2

(a) Variation in lattice parameters with pressure. Here, horizontal arrows point to the corresponding vertical axis. The inset shows pressure variations of the c/a ratio. The curves fitting the $P\text{–}V$ data using the third-order BM equation are shown by solid lines in (b). The inset in (b) shows the variations of the weight fraction of the $2H_a^{\prime }$ phase with pressure. The vertical dashed lines are a guide to the eye. Error bars are less than the size of symbols marking data points.

Figure 3

(a) Evolution of Raman spectra with pressure in the forward cycle. Solid lines are the Lorentzian fits to the experimental data points. (b) Frequencies of the Raman modes as a function of pressure. Solid lines are linear fits $[{\omega }_p={\omega }_0+\left(\frac{d\omega }{dP}\right)P]$ to the observed frequencies, and the values of slopes are given. Error bars (obtained from the fitting procedure) are also shown. Vertical dashed lines mark the transitions.

Figure 4

(a) The frequency difference plot of the $A_1^2$ ($A_{1g}$ of ${\mathrm{MoS}}_2$ type) and $E_1^2$ ($E_{2g}^1$ of ${\mathrm{MoS}}_2$ type) modes. (b) Calculated frequency difference plot for the $A_1^2$ and $E_1^2$ Raman modes as a function of pressure.

Figure 5

Layered crystal structures of bulk MoSSe with different stacking sequences: (a) ${\mathrm{AbA}}^{\prime }{\mathrm{BaB}}^{\prime }$ [$2H_c^{\prime }$; space group (SG): ${P6}_{3}mc$], (b) ${\mathrm{AbA}}^{\prime }{\mathrm{B}}^{\prime }\mathrm{aB}$ (SG: $P\text{–}3m1$), (c) ${\mathrm{AbA}}^{\prime }{\mathrm{A}}^{\prime }\mathrm{bA}$ (SG: $P\text{–}6m2$), and (d) ${\mathrm{AbA}}^{\prime }{\mathrm{AbA}}^{\prime }$ (SG: $P3m1$). A and B label sites of S atoms, a and b label sites of Mo atoms, and ${\mathrm{A}}^{\prime }$ and ${\mathrm{B}}^{\prime }$ label sites of Se atoms. (e) Construction of $2H_a^{\prime }$ (SG: ${P6}_{3}mc$) from the $2H_c^{\prime }$ structure by sliding the top layer in the $y$ direction while keeping the bottom layer fixed (in a given unit cell). (f) Calculated $c/a$ ratio of bulk $2H_c^{\prime }$ MoSSe. (g) Indirect band gap between bands at $\mathrm{\Gamma }$ and at the midpoint of $\mathrm{\Gamma }\text{–}K$ and (h) a direct band gap at the $K$ point of bulk $2H_c^{\prime }$ MoSSe as a function of pressure. Note that the indirect band gap closes at $P\sim 26$ GPa.

Figure 6

Isosurfaces of wave functions at VBM-1 and VBM at the $\mathrm{\Gamma }$ point at (a) $P=0$ GPa, (b) 4 GPa, (c) 8 GPa, and (d) 12 GPa. The isosurface of the VBM does not show any change with pressure, but the VBM-1 isosurface shows significant changes with pressure. The $d$ orbital contribution of Mo atoms decreases with increasing pressure and disappears completely at $P\ge 8$ GPa. The wave function at VBM-1 shows mixed symmetry at $P\le 4$ GPa and odd symmetry at $P>4$ GPa under mirror reflection. Note that the mirror plane is at the Mo atom in the plane of the paper.

Figure 7

Difference in enthalpies of $2H_a^{\prime }$ and $2H_c^{\prime }$ structures of MoSSe, showing a reversal of their relative stability at 26.6 GPa (at 0 K). The right inset shows the structure of $2H_a^{\prime }$ in top and side views. Note that in the top view of the $2H_a^{\prime }$ structure, the Se atom at the center of the hexagon appears from the bottom layer. The probability $\mathbb{P}(T=300$ K) of MoSSe to be in the $2H_a^{\prime }$ phase as a function of pressure is shown in the left inset.