Tunable Superconductivity in 1313-La${}_3$Ni${}_2$O${}_7$: Suppressed under Compression and Possible $s^{\pm }$ Pairing under Tension

Motivated by recent progress in the 1313-La${}_3$Ni${}_2$O${}_7$ nickelate thin films (Nie et al., Nature {\bf 652}, 628 (2026)), we systematically investigate the effects of both compressive and tensile strain in this system. Self-doping effects between the single-layer (SL) and trilayer (TL) blocks are observed in our studies in both cases, but are most pronounced under tensile strain. We find that superconductivity is unlikely to emerge in the 1313 film on the LSAO substrate even with further hole doping. Remarkably, within the random-phase approximation, under {\it tensile} strain, a robust $s^{\pm }$-wave pairing state emerges in the TL subsystem with sign changes between the small electron-like $\sigma$ pocket at the $\mathrm{\Gamma }$ point and the small hole-like $\gamma$ pocket at the M point. These pockets are connected by a wave vector close to $(\pi ,\pi )$. Our calculations also suggest that superconductivity in 1313-LNO requires an optimally sized $\gamma$ pocket, because an oversized $\gamma$ pocket suppresses pairing formation. Overall, our results predict strain-dependent electronic reconstruction in 1313-La${}_3$Ni${}_2$O${}_7$ and provide guiding principles for engineering superconductivity under ambient pressure conditions.