Superconductivity in tin selenide under pressure

Tin selenide is a layered material that captured the interest of the scientific community for its stunning thermoelectric properties and fascinating phase transitions under pressure. Recently, an experimental study revealed the existence of a topological and superconducting phase in its pressure-stabilized CsCl-type phase. By means of ab initio techniques, we investigate the structural properties of this compound and its pressure phase diagram, comparing our findings with the experimental results. We then focused on the electronic features of the topological CsCl-type phase and analyze its dynamical and superconducting properties. To understand the origin of the superconducting transition, we predict the critical temperature as a function of the pressure, $T_c$(P), by the superconducting density-functional theory and analyze the behavior of the resistance with pressure and temperature by means of a percolative model. The careful comparison of calculations with available experiments reveals that inhomogeneities and nonhydrostatic pressure effects are relevant in this system.

Figure 1

$Pnma$ GeS-type [panel (a)], $\gamma \text{−}Pnma$ [panel (b)], CsCl-type [panel (c)], $Cmcm$ [panel (d)], and NaCl-type [panel (e)] structures [20]. Red and blue atoms are Sn and Se, respectively.

Figure 2

Volume-pressure [panel (a)] and enthalpy-pressure phase diagram of SnSe [panel (b)]. Vertical dashed lines highlight $\gamma \text{−}Pnma$ to $Cmcm$ and $Cmcm$ to $Pm\overline{3}m$ CsCl-type structural transitions.

Figure 3

Comparison between experimental (points) and theoretical (lines) pressure evolution of the lattice parameters of the GeS-type phase [panel (a)], experimental data from Ref. [22], the $z$(Sn) coordinate of the GeS-type phase [panel (b)], and the lattice parameter of the CsCl-type phase [panel (c)], experimental data from Ref. [21].

Figure 4

Band structure of the CsCl-type phase of SnSe at 50 GPa without SOC [panel (a)]. Band structure with SOC projected on atomic Sn($s$) (red) and atomic Sn($p$) (blue) orbitals at 20 GPa [panel (b)] and 40 GPa [panel (c)].

Figure 5

Evolution of the DOS for the CsCl-type phase calculated at different pressures. Inset: DOS at Fermi level as a function of the pressure (states/eV/SnSe).

Figure 6

Phonon dispersion for the CsCl-type phase at 30 GPa (solid) and 50 GPa (dashed) (panel (a)]. Corresponding DOS [panel (b)] and Eliashberg function [panel (c)].

Figure 7

Supeconducting gap (${\mathrm{\Delta }}_{sc}$) as a function of the temperature at various pressures [panel (a)]. Critical temperature of the CsCl-type phase and $\lambda$ (inset) as a function of the pressure [panel (b)]. Red squares are the experimental values of the onset temperature. The shadowed area corresponds to the pressure range where the CsCl phase is not the ground state. Lines are a guide to the eye.

Figure 8

Fermi surface for the CsCl-type phase at 30 GPa. $\mathrm{\Gamma }$ and R points are at the center and at the corner of the cube, respectively.

Figure 9

EMA fit of the experimental resistance data from Ref. [22] at different values of the nominal pressure. The dashed line indicates a representative value of $T_c^{\text{onset}}$ at 27.3 GPa.

Figure 10

Parameters ($P_m$, $\sigma$) extracted from the fit of resistance curves shown in Fig. 9 with Eq. (8). In the inset, the SC fraction $w_s$.

Figure 11

Superconducting critical temperature as a function of the rhombohedral angle at 50 GPa. Numbers near the symbols represent the in-plane/out-plane components of the stress tensor in the rhombohedral phase in the hexagonal representation.