Carrier mobilities and electron-phonon interactions beyond DFT
(2026) npj Computational Materials — Vol. 12, n° 1, p. 151 (2026)
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- Electron-phonon coupling is a key interaction that governs diverse physical processes such as carrier transport, superconductivity, and optical absorption. Calculating such interactions from first-principles with methods beyond density-functional theory remains a challenge. We introduce here a finite-difference framework for computing electron-phonon couplings for any electronic structure method that provides eigenvalues and eigenvectors, and showcase applications for hybrid and Koopmans functionals, and GW many-body perturbation theory. Our approach introduces a novel projectability scheme based on eigenvalue differences and bypasses many of the limitations of the direct finite difference methods. It also leverages symmetries to reduce the number of independent atomic displacements, decreasing overall computational cost. This approach enables seamless integration with established first-principles codes for generating displaced supercells, performing Wannier interpolations, and evaluating transport properties. Applications to silicon and gallium arsenide show that advanced electronic-structure functionals predict different electron-phonon couplings and modify band curvatures, resulting in much more accurate estimates of intrinsic carrier drift mobilities and effective masses. In general, our method provides a robust and accessible framework for calculating the electron-phonon properties with state-of-the-art beyond DFT methods. Electron-phonon interactions play a central role in determining fundamental materials' properties, such as electron and hole mobilities 1-3 , superconductivity 4 , band renormalization 5 , and non-adiabatic effects 6. Accurate modeling of these interactions is essential for advancing technologies ranging from efficient electronic devices to novel superconducting materials. First-principles calculations of electron-phonon couplings based on density-functional theory (DFT) have reached a maturity level that even allows high-throughput calculations 5. A key step in these approaches is the evaluation of electron-phonon matrix elements, which quantify the effective interactions between electrons and phonons 4,7. Computationally, two approaches exist for this task: density-functional perturbation theory (DFPT) 8,9 and the finite difference (FD) method 10-12. Recent work suggests machine learning as another promising alternative, as it allows accurate results when trained on relatively small datasets 13,14. Although DFPT is generally a more computationally efficient approach than FD methods, as it offers favorable scaling and access to arbitrary phonon wavevectors q, it requires dedicated and involved implementations. For this reason, pertur-bative approaches based on DFPT have only recently been applied to specific beyond-DFT methods, such as DFT+U 15-17 and G 0 W 0 18,19. Up to now, most of the calculations on the electron-phonon-related properties have been performed using DFPT with semilocal DFT functionals, and this method is considered to be the state of the art. Notwithstanding its success, discrepancies persist between first-principles predictions based on DFPT and experimental observations for many electron-phonon related properties 5,20,21. This is partially due to the fact that Kohn-Sham (KS) DFT does not provide reliable quasiparticle energies and other excited-state properties 22-24. To address this, more advanced methods have been developed to improve the description of quasiparticle energies. These include the incorporation of a fraction of exact exchange 25,26 , the enforcement of pie-cewise linearity conditions 27-32 , and the inclusion of many-body effects 18,33,34. Improved electronic structure approaches were reported to affect electron-phonon properties 19,35,36 , but their impact on carrier mobility needs to be better understood. For these reasons, there is a growing need for a more straightforward and general method to calculate electron-phonon couplings. For a long time, finite differences have been successfully used to predict phonon properties with any functional, and today, well-established codes exist that implement these developments 37-39. However, the absence of community codes to perform a similar task for electron-phonon properties
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Poliukhin, A., Colonna, N., Libbi, F., Poncé, S., & Marzari, N. (2026). Carrier mobilities and electron-phonon interactions beyond DFT. npj Computational Materials, 12(1), 151. https://doi.org/10.1038/s41524-026-02011-2 (Original work published 2026)