Pressure-induced structural transition, metallization, and topological superconductivity in PdSSe

Pressure not only provides a powerful way to tune the crystal structure of transition-metal dichalcogenides (TMDCs) but also promotes the discovery of exotic electronic states and intriguing phenomena. Structural transitions from the quasi-two-dimensional layered orthorhombic phase to three-dimensional cubic pyrite phase, metallization, and superconductivity under high pressure have been observed experimentally in TMDC materials ${\mathrm{PdS}}_2$ and ${\mathrm{PdSe}}_2$. We report a theoretical prediction of the pressure-induced evolutions of crystal structure and electronic structure of PdSSe, an isomorphous intermediate material of the orthorhombic ${\mathrm{PdS}}_2$ and ${\mathrm{PdSe}}_2$. A series of pressure-induced structural phase transitions from the layered orthorhombic structure into an intermediate phase and then to a cubic phase is revealed. The intermediate phase features the same structure symmetry as the ambient orthorhombic phase, except for drastic collapsed interlayer distances and striking changes of the coordination polyhedron. Furthermore, the structural phase transitions are accompanied by electronic structure variations from semiconductor to semimetal, which are attributed to bandwidth broadening and orbital-selective mechanisms. Specifically, the cubic phase PdSSe is distinct from the cubic ${\mathrm{PdS}}_2$ and ${\mathrm{PdSe}}_2$ materials by breaking inversion and mirror-plane symmetries but showing similar superconductivity under high pressure, which originates from strong electron-phonon coupling interactions concomitant with topologically nontrivial Weyl and high-fold fermions. The intricate interplay between lattice, charge, and orbital degrees of freedom as well as the topologically nontrivial states in these compounds will further stimulate wide interest to explore the exotic physics of the TMDC materials.

Figure 1

Three polymorphs of PdSSe in (a) $AA$, (b) $AB$, and (c) $BB$ stacking manner with gradually increasing energy. The big gray balls represent Pd atoms, while the small yellow (green) balls represent S (Se) atoms.

Figure 2

Evolutions of crystal structure and electronic structure of PdSSe under hydrostatic pressure: (a) lattice constants, (b) interatomic distances (the inset illustrates the coordination environment of the Pd atom), (c) volume, and (d) energy changes as a function of pressure and crystal structure with coordination polyhedra at (e) 0 GPa, (f) 4 GPa, and (g) slices of the electron localization function at different pressures.

Figure 3

The electronic structure of PdSSe under different hydrostatic pressures: (a) band structures calculated by HSE06. The contributions of the $d_{x^2-y^2}$ (blue balls) and $d_{z^2}$ (red balls) orbitals are proportional to the size of the colored balls. (b) The corresponding partial charge density. The selected energy range of the bands that are used for the evaluation of the partial charge density is set to −1 to 0 eV.

Figure 4

Comparisons of the band structure of the cubic-phase (a) ${\mathrm{PdS}}_2$, (b) PdSSe ($AA$ polymorph), and (c) ${\mathrm{PdSe}}_2$ at pressure of 4 GPa without (w/o) or with SOC interactions. The green rhombus illustrates the charge gap along the Γ-$R$ directions. The Dirac and nodal-line states are marked by the red circles in (a) and (c), while they are broken as indicated by the blue circles in (b). The cyan points mark the fourfold and sixfold degenerate fermions at the Γ point and $R$ point. The Weyl points along the Γ-$R$ line are highlighted by the shadow rectangles in (b), which are enlarged as shown in Fig. S8 [60].

Figure 5

Calculated (a) phonon density of states (PhDOS) and (b) Eliashberg electron-phonon coupling spectral function ${\alpha }^{2}F\left(\omega \right)$ and the electron-phonon coupling integral λ(ω) of cubic PdSSe at 4 GPa.

Figure 6

The evolutions of (a) electron-phonon coupling constants and (b) superconducting critical temperatures of ${\mathrm{PdS}}_2$, PdSSe, and ${\mathrm{PdSe}}_2$ along with pressure. The data drawn in green come from our previous theoretically calculated results [35].