Structural phase transition, $s_{\pm }$-wave pairing and magnetic stripe order in the bilayered nickelate superconductor La${}_3$Ni${}_2$O${}_7$ under pressure

Motivated by the recently discovered high-$T_c$ superconductor La${}_3$Ni${}_2$O${}_7$, we comprehensively study this system using density functional theory and random phase approximation calculations. At low pressures, the Amam phase is stable, containing the Y${}^{2-}$ mode distortion from the Fmmm phase, while the Fmmm phase is unstable. Because of small differences in enthalpy and a considerable Y${}^{2-}$ mode amplitude, the two phases may coexist in the range between 10.6 and 14 GPa, beyond which the Fmmm phase dominates. In addition, the magnetic stripe-type spin order with wavevector ($\pi$, 0) was stable at the intermediate region. Pairing is induced in the $s_{\pm }$-wave channel due to partial nesting between the {\bf M}=$(\pi ,\pi )$ centered pockets and portions of the Fermi surface centered at the {\bf X}=$(\pi ,0)$ and {\bf Y}=$(0,\pi )$ points. This resembles results for iron-based superconductors but has a fundamental difference with iron pnictides and selenides. Moreover, our present efforts also suggest that La${}_3$Ni${}_2$O${}_7$ is qualitatively different from infinite-layer nickelates and cuprate superconductors.