Unifying Strain-driven and Pressure-driven Superconductivity in La$_{3}$Ni$_{2}$O$_{7}$: Suppressed charge/spin density waves and enhanced interlayer coupling

Recent strain-stabilized superconductivity at ambient pressure in La$_3$Ni$_2$O$_{7}$ films opens new avenues for nickelates research, in parallel with its pressure-induced counterpart. Using density functional theory calculations, we elucidate the critical factors bridging strain- and pressure-driven superconductivity in La$_3$Ni$_2$O$_{7}$ by comprehensively analyzing structural, electronic, magnetic, and density wave characteristics. Consistent with recent scanning transmission electron microscopy observations, we find an $I4/mmm$ structural transition at $-0.9\%$ strain, preceding superconductivity onset. Electronic analysis shows compressive strain lowers Ni-$d_{z^2}$ orbital energy levels, while interfacial Sr diffusion effectively reconstructs the $d_{z^2}$ pockets, quantitatively matching angle-resolved photoemission spectroscopy experiments. The interlayer antiferromagnetic coupling $J_\perp$ under pressure or strain closely tracks experimental superconducting $T_c$ variation. The dome-shaped pressure dependence and monotonic strain dependence of $J_\perp$ mainly arise from modulations in the apical oxygen $p_z$ energy levels. Moreover, compressive strain suppresses both charge density waves (CDW) and spin density waves (SDW) instabilities analogous to pressure effects, with SDW vanishing concurrently with the structural transition and CDW disappearing at $\sim-3.3\%$ strain. Our results indicate that suppressed density waves and enhanced $J_\perp$ are crucial for both strain- and pressure-driven superconductivity. Accordingly, we propose several candidate substrates capable of achieving greater compressive strain, thereby potentially increasing $T_c$.