Computational methods for predicting Tc

This post will focus on the methods available to predict/derive $T_c$ of a material. We want to be able to build a pipeline where we can go beyond the available (and experimental) Tc data and train a model to estimate whichever first-principles (or close to it) method.

We're tracking ML-based methods, but as we have learned we are pretty limited by the SuperCon dataset and its derivations.

Because superconductivity is not very well understood in Type-II superconductors, our options are pretty limited.

1. Density Functional Theory (DFT) Combined with BCS Theory

• Calculates electron-phonon coupling strength (λ) and phonon frequencies from first principles

• Uses Allen-Dynes or McMillan formula to estimate $T_c$

• Most reliable for conventional superconductors where electron-phonon coupling is the main mechanism

• Limited accuracy for unconventional superconductors

2. Eliashberg Theory

• More sophisticated extension of BCS theory

• Accounts for retardation effects and strong coupling

• Can provide more accurate Tc predictions than simple BCS

• Computationally more intensive than BCS-based approaches

3. Ab Initio Crystal Structure Prediction

• Predicts stable crystal structures under pressure

• Combined with electron-phonon calculations for Tc estimation

• Particularly useful for hydrides under pressure

• Successfully predicted high-Tc in $H_3S$ and $LaH_{10}$

4. Temperature ramping, first-principles property estimation then correlation.

• Run AIMD/MLIP at different temperatures

• Extract ensemble of structures

• Calculate chosen properties for each snapshot

• Look for signatures that correlate with known Tc values in training set

• Use these correlations to predict Tc in new materials