Unusual Pressure-Induced Periodic Lattice Distortion in ${\mathrm{SnSe}}_2$

We performed high-pressure x-ray diffraction (XRD), Raman, and transport measurements combined with first-principles calculations to investigate the behavior of tin diselenide (${\mathrm{SnSe}}_2$) under compression. The obtained single-crystal XRD data indicate the formation of a $(1/3,1/3,0)$-type superlattice above 17 GPa. According to our density functional theory results, the pressure-induced transition to the commensurate periodic lattice distortion (PLD) phase is due to the combined effect of strong Fermi surface nesting and electron-phonon coupling at a momentum wave vector $\mathbf{q}=(1/3,1/3,0)$. In contrast, similar PLD transitions associated with charge density wave (CDW) orderings in transition metal dichalcogenides (TMDs) do not involve significant Fermi surface nesting. The discovered pressure-induced PLD is quite remarkable, as pressure usually suppresses CDW phases in related materials. Our findings, therefore, provide new playgrounds to study the intricate mechanisms governing the emergence of PLD in TMD-related materials.

Figure 1

XRD patterns below (a) and above (b) the phase transition. The sudden appearance of superlattice peaks [magenta circles in (b)] is indicative for a $\sqrt{3}\times \sqrt{3}\times 1$ superlattice formation. (c) The pressure dependence of the lattice parameters $a$ (black squares, left axis) and $c$ (red circles, right axis). The inset shows the pressure dependence of the volume per one formula unit ($V/Z$). For comparison with the $H1$ phase, $a$ in the $H2$ phase was rescaled by $1/\sqrt{3}$. Small kinks are observed in $c$ and $V/Z$ at 17 GPa.

Figure 2

(a) Calculated softening of the lowest-energy (degenerate) phonon modes, where imaginary phonon frequencies are shown as negative, illustrating the pressure-induced destabilization of the $H1$ phase. The inset shows the squared frequency of the modes. (b) Differences in enthalpies for the considered structures as function of pressure, where the $H1$ phase was chosen as reference.

Figure 3

(a) Selected Raman spectra for various pressures. New modes appear above 17 GPa, indicating the $H1\text{−}\mathrm{to}\text{−}H2$ phase transition. (b) Calculated and measured frequency dependence of the Raman-active modes as a function of pressure. The theoretical results are shown as red symbols ($H1$), green symbols ($H2\text{−}1$), and blue symbols ($H2\text{−}2$). For $H1$, the data before and after the phase transition are shown as filled and open symbols, respectively. The experimental data are shown as black symbols.

Figure 4

(a) The FS contribution to the adiabatic phonon self-energy, (b) the static bare susceptibility in the constant matrix approximation, and (c) the EPC strength for the soft phonon mode in the three-atom $H1$ structure at various pressures [72]. These results provide evidence that both FS nesting and electron-phonon interactions play crucial parts in the observed phase transition of ${\mathrm{SnSe}}_2$.