Electronic, vibrational, and electron-phonon coupling properties in SnSe$_2$ and SnS$_2$ under pressure

The tin-selenide and tin-sulfide classes of materials undergo multiple structural transitions under high pressure leading to periodic lattice distortions, superconductivity, and topologically non-trivial phases, yet a number of controversies exist regarding the structural transformations in these systems. We perform first-principles calculations within the framework of density functional theory and a careful comparison of our results with available experiments on SnSe$_2$ reveals that the apparent contradictions among high-pressure results can be attributed to differences in experimental conditions. We further demonstrate that under hydrostatic pressure a $\sqrt{3} \times \sqrt{3} \times 1$ superstructure can be stabilized above 20 GPa in SnS$_2$ via a periodic lattice distortion as found recently in the case of SnSe$_2$, and that this pressure-induced phase transition is due to the combined effect of Fermi surface nesting and electron-phonon coupling at a momentum wave vector $\mathbf{q}$ = $(1/3, 1/3, 0)$. In addition, we investigate the contribution of nonadiabatic corrections on the calculated phonon frequencies, and show that the quantitative agreement between theory and experiment for the high-energy $A_{1g}$ phonon mode is improved when these effects are taken into account. Finally, we examine the nature of the superconducting state recently observed in SnSe$_2$ under nonhydrostatic pressure and predict the emergence of superconductivity with a comparable critical temperature in SnS$_2$ under similar experimental conditions. Interestingly, in the periodic lattice distorted phases, the critical temperature is found to be reduced by an order of magnitude due to the restructuring of the Fermi surface.