Novel high pressure structures and superconductivity of niobium disulfide

We have investigated the pressure-induced phase transition and superconducting properties of niobium disulfide (NbS$_2$) based on the density functional theory. The structures of NbS$_2$ at pressures from 0 to 200 GPa were predicted using the multi-algorithm collaborative (MAC) structure prediction technique. The previously known 1$T$-, 2$H$-, and 3$R$-NbS$_2$ were successfully reproduced. In addition, many metastable structures which are potential to be synthesized were also discovered. Based on the enthalpy calculations, we found that at 26 GPa NbS$_2$ transits from the double-hexagonal (2$H$) structure to the tetragonal $I4/mmm$ structure with a $10.6\%$ volume reduction. The calculated elastic constants and phonon dispersion curves of $I4/mmm$-NbS$_2$ confirm its mechanical and dynamical stability at high pressure. More interestingly, the coordination number of Nb in $I4/mmm$ structure is eight which is larger than that in the traditional metal dichalcogenides, indicating a new type of bondings of Nb and S atoms. In the new Nb-S bondings, one Nb atom and neighboring eight S atoms form a [NbS$_8$] hexahedron unit. Furthermore, $I4/mmm$-NbS$_2$ exhibits a higher superconducting critical temperature than 2$H$-NbS$_2$, as is resulted from the stronger electron-phonon coupling coefficients