IsoME: Streamlining high-precision Eliashberg calculations

This paper introduces the Julia package ISOME, an easy-to-use yet accurate and robust computational tool designed to calculate superconducting properties. Multiple levels of approximation are supported, ranging from the basic McMillan-Allen-Dynes formula and its machine learning-enhanced variant to Eliashberg theory, including static Coulomb interactions derived from GW calculations, offering a fully ab initio approach to determine superconducting properties, such as the critical superconducting temperature (T _c) and the superconducting gap function (Δ). We validate ISOME by benchmarking it against various materials, demonstrating its versatility and performance across different theoretical levels. The findings indicate that the previously held assumption that Eliashberg theory overestimates T _c is no longer valid when μ ^⁎ is appropriately adjusted to account for the finite Matsubara frequency cutoff. Furthermore, we conclude that the constant density of states (DOS) approximation remains accurate in most cases. By unifying multiple approximation schemes within a single framework, ISOME combines first-principles precision with computational efficiency, enabling seamless integration into high-throughput workflows through its T _c search mode. This makes ISOME a powerful and reliable tool for advancing superconductivity research. Program summary: Program Title: ISOME CPC Library link to program files: https://doi.org/10.17632/frwsdxf44s.1 Developer's repository link: https://github.com/cheil/IsoME.jl Licensing provisions: MIT license Programming language: Julia 1.10 or higher Supplementary material: https://cheil.github.io/IsoME.jl Nature of problem: The challenge addressed by ISOME is the rigorous, first-principles calculation of superconducting properties, particularly the critical temperature (T _c) and detailed self-energy components. Predicting these properties involves solving the highly nonlinear, coupled Migdal-Eliashberg equations that capture the interplay between electron-phonon interactions and Coulomb repulsion. This is nontrivial because the equations require careful treatment of frequency-dependent interactions, accurate sampling of the electronic density of states near the Fermi level, and efficient summation over extensive Matsubara frequencies. Additionally, incorporating energy-dependent screening effects and ensuring numerical convergence across multiple energy scales further complicates the task. Addressing these issues is essential not only for understanding the fundamental physics of superconductivity but also for guiding the discovery and design of new superconducting materials. Solution method: ISOME employs isotropic Migdal-Eliashberg theory as its backbone, implementing a hierarchical approach that spans several levels of approximation. At the simplest level, the code uses semi-empirical formulas such as the McMillan-Allen-Dynes equation enhanced by machine learning to provide quick estimates of T _c. For more detailed studies, it solves self-consistently the full set of Eliashberg equations using either a constant or variable density of states (DOS) approximation, with the possibility to include the full energy-dependent static Coulomb interaction computed via GW methods. The package is written in Julia, ensuring high computational efficiency and ease of integration into high-throughput workflows. It further incorporates sparse-sampling techniques to accelerate Matsubara frequency summations and an automated T _c search mode, thereby balancing computational cost with high-precision predictions. Additional comments including restrictions and unusual features: ISOME is an open-source Julia package designed for high-throughput superconductivity investigations. Its modular architecture supports diverse approximation schemes that balance efficiency and accuracy. However, robust predictions require high-quality input data and thorough convergence testing, particularly for systems with complex electronic structures or strong energy-dependent interactions near the Fermi level.