Microscopic theory for electron-phonon coupling in twisted bilayer graphene

This dataset provides the underlying numerical results from a first-principles-based microscopic theory investigating electron-phonon coupling in twisted bilayer graphene. This data package specifically catalogs the electron-phonon interactions, Eliashberg functions, and mode-specific coupling strengths generated via a momentum-space continuum model.
Dataset structure and contents: The data is organized into three primary compressed directories representing the evolution of EPC from the atomic to the macroscopic scale:
EPC Constants and Eliashberg Functions (lambda.zip): Contains .mat files indexed by twist angle (\theta). Key variables include the Eliashberg function (\alpha^2F) and EPC constants (\lambda) calculated under both adiabatic and non-adiabatic frameworks, allowing for comparison of dynamical effects near the magic angle.
Mode-Averaged Matrix Elements (g_avg_new.zip): Data identifying the contribution of specific phonon branches to the total coupling strength.
Phonon Dispers..., , # Data from: Microscopic theory for electron-phonon coupling in twisted bilayer graphene

Dataset DOI: [10.5061/dryad.t76hdr8f9](https://doi.org/10.5061/dryad.t76hdr8f9)

## Description of the data and file structure

This dataset contains the numerical outputs of a first-principles-based microscopic theory designed to evaluate the electron-phonon coupling in twisted bilayer graphene. The model utilizes a momentum-space continuum approach, bypassing the computational cost of periodic supercells. The results include calculations within the generalized Eliashberg-McMillan framework, providing a comparison between adiabatic approximations and a full non-adiabatic treatment of the moiré flat bands. Here, we include the data necessary to reproduce the key results. 

## 1. Filename: lambda.zip

**Description:** lambda.zip contains the calculated electron-phonon coupling (EPC) constant and Eliashberg function. 

Variables in lambda_<<theta_deg>>.mat files: 

* `E_list`: list of Fermi energies ...,