Strain-Vacancy Engineering Model (SVEM) for Enhanced Superconductivity in La₃Ni₂O₇ Thin Films: A Pathway to 100K 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. The model relates Tc to strain (ε) and oxygen vacancy concentration (δ) via: Tc(ε, δ) = Tc,0 (1 + α ε + β ε²) exp(−kvac δ) where Tc,0 = 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 > 0.95 and RMSE = 3.2K. For optimized synthesis conditions—compressive strain ε = −10% and ultra-low oxygen vacancy concentration δ < 0.005—the model predicts Tc ≈ 95-110K, 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.本研究提出一种现象学应变-空位工程模型（Strain-Vacancy Engineering Model，SVEM），通过双轴应变与氧化学计量比的协同调控，实现对外延La₃Ni₂O₇薄膜中超导临界转变温度（Tc）的预测与调控。基于近期实验观测结果——高压下Tc≈80K、常压下应变薄膜中Tc≈26~42K，我们构建了具有物理依据的统一框架，将两类现象整合为单一预测方程。该模型通过如下关系式将Tc与应变（ε）及氧空位浓度（δ）关联起来： Tc(ε, δ) = Tc,0 (1 + α ε + β ε²) exp(−kvac δ) 其中Tc,0=48K为基准临界转变温度，α≈9.5 K/%表征线性应变耦合效应，β≈−15 K/%²用于描述大形变下的应变饱和效应，kvac≈15则量化了氧空位带来的指数型抑制作用。针对文献数据的验证结果显示，该模型的决定系数R²>0.95，均方根误差RMSE=3.2K。 在优化合成条件下，即施加ε=−10%的压应变且氧空位浓度δ<0.005时，模型预测Tc≈95~110K，这意味着常压下镍酸盐超导材料的超导性能可实现具有实验可行性的显著提升。我们还提供了用于验证上述预测的详细合成方案（包括分子束外延、衬底选择与氧退火工艺）与表征路线图（涵盖X射线衍射、电子显微术与输运性能测试）。 本研究确立了SVEM作为下一代镍酸盐超导材料理性设计的定量工具，填补了高压超导发现与技术实用化薄膜制备之间的研究空白。 关键词：镍酸盐超导体、La₃Ni₂O₇、应变工程、氧空位、外延薄膜、临界转变温度提升、现象学建模。