Simplified function for predicting superconducting critical temperature

Currently, there is intense competition to develop models that can accurately estimate the critical temperature across a wide range of superconductors, while striving for straightforward derivations and comprehensive predictions. In this work, we present an approach to determining the critical temperature based on the linearized Eliashberg gap equations employing the bandwidth model. To verify the accuracy of our model, we collect Eliashberg spectral functions from various independent studies, compute the necessary parameters, and solve the Eliashberg gap equations numerically to obtain the exact solutions, along with utilizing the modified Allen-Dynes equation. The findings suggest that both models are in good agreement and exhibit a strong correlation with the exact solutions, although minor deviations are observed. The present study may provide a more effective approach to predicting the critical temperature of superconductors, particularly for materials exhibiting elevated transition temperatures, in future investigations.