Came across this workflow researching some permanent magnet work. I haven't fully explored the code or how much this work will help, but sharing here to reference later because stuff is hard to find on Zenodo.
https://zenodo.org/records/12685941
HamEPC is a machine learning workflow that leverages the HamGNN framework to efficiently calculate the electron-phonon coupling (EPC). By utilizing atomic orbital-based Hamiltonian matrices and gradients predicted by HamGNN, HamEPC is able to significantly accelerate EPC calculations compared to traditional density functional perturbation theory (DFPT) methods. HamEPC can be employed to evaluate important materials properties, including the electron-phonon coupling matrix, carrier mobility, and superconducting transition temperature.
Given we can generate the electron-phonon coupling matrix, we can then derive our way to Tc.
The coupling matrix describes how electrons interact with lattice vibrations (phonons), which is the microscopic mechanism behind conventional superconductivity.
In the BCS theory framework, superconductivity arises when electrons form Cooper pairs through an attractive interaction mediated by phonons. When an electron moves through a crystal lattice, it slightly distorts the lattice due to Coulomb attraction with positive ions. This distortion creates a region of higher positive charge density that can attract another electron, effectively creating an indirect attractive interaction between electrons despite their natural Coulomb repulsion.
The electron-phonon coupling matrix elements quantify the strength of this interaction. Computationally, these are calculated using:
First-principles approaches: Density functional perturbation theory (DFPT) is commonly used to compute phonon frequencies and electron-phonon matrix elements from first principles. The coupling strength is characterized by the Eliashberg function α²F(ω), which depends on these matrix elements.
Key computational quantities:
The average electron-phonon coupling constant λ, which determines the superconducting transition temperature Tc through the McMillan formula or more sophisticated Eliashberg equations
Mode-specific coupling strengths that identify which phonon modes contribute most to pairing
Momentum-resolved coupling that reveals anisotropic pairing mechanisms
Materials design applications: Computational screening uses these calculations to predict new superconductors by identifying materials with strong electron-phonon coupling while maintaining sufficient electronic density of states at the Fermi level. This has guided discoveries in systems like metal hydrides under pressure, where extremely strong coupling can lead to high-Tc superconductivity.
The matrix elements also help distinguish between conventional phonon-mediated superconductivity and unconventional mechanisms, making them essential for understanding and predicting superconducting materials computationally.