Strain-Vacancy Engineering Model (SVEM) for Enhanced Superconductivity in La₃Ni₂O₇ Thin Films: A Pathway to 80K Critical Temperature

We propose a phenomenological Strain-Vacancy Engineering Model (SVEM) to predict and control the critical temperature (Tc) in epitaxial La₃Ni₂O₇ thin films through coupled tuning of biaxial strain and oxygen stoichiometry. Building upon recent experimental observations of Tc ≈ 80K under high pressure and Tc ≈ 26-42K in strained thin films at ambient pressure, we develop a physically-motivated framework that unifies these phenomena into a single predictive equation: Tc(ε, δ) = Tc₀ (1 − α ε + β ε²) exp(−kvac δ) where Tc₀ = 48K represents the baseline critical temperature, α ≈ 9.5 K/% captures linear strain coupling, β ≈ −15 K/%² accounts for strain saturation at large deformations, and kvac ≈ 15 quantifies exponential suppression by oxygen vacancies. Validation against literature data yields R² = 0.951 and RMSE = 2.5K. For optimized synthesis conditions—compressive strain ε = −10% and ultra-low oxygen vacancy concentration δ < 0.005—the model predicts Tc ≈ 80K, representing a realistic and experimentally achievable enhancement of superconductivity in nickelates at ambient pressure. We provide detailed synthesis protocols (molecular beam epitaxy, substrate selection, oxygen annealing) and characterization roadmaps (X-ray diffraction, electron microscopy, transport measurements) to validate these predictions. This work establishes SVEM as a quantitative tool for rational design of next-generation nickelate superconductors, bridging the gap between high-pressure discoveries and technologically relevant thin-film implementations. Keywords: Nickelate superconductors, La₃Ni₂O₇, strain engineering, oxygen vacancies, epitaxial thin films, critical temperature enhancement, phenomenological modeling.