Strain-tuned structural, electronic, and superconducting properties of thin-film La$_3$Ni$_2$O$_7$

Abstract: The recent discovery of high-temperature superconductivity in La$3$Ni$_2$O$_7$ under ambient-pressure in strained thin films raises the question of how superconductivity can be optimized through strain. In this work, we investigate the strain-dependent electronic structure and superconducting transition temperature ($T_c$) of La$_3$Ni$_2$O$_7$ using density functional theory combined with random phase approximation spin-fluctuation calculations. We find that biaxial strain acts as a tuning parameter for Fermi surface topology and magnetic correlations. Large tensile strain drives a Lifshitz transition characterized by a $d{z^2}$ band crossing, leading to a sharp increase in the density of states and theoretical pairing strength. However, this is accompanied by a large increase in magnetic proximity, suggesting strong competition with spin-density-wave order. Conversely, under compressive strain, we identify a structurally selective $T_c$ enhancement restricted to the high-symmetry $I4/mmm$ phase. This effect is driven by the straightening of Ni--O--Ni bonds and the emergence of a $Γ$-centered hole pocket, yielding $T_c$ values consistent with recent thin-film experiments. Our results highlight the balance between structural symmetry, electronic topology, and magnetic instability in nickelates, and provides a theoretical framework for optimizing superconductivity via strain engineering.