Intraband electron-phonon coupling via finite-difference methods

Electron–phonon coupling (EPC) underpins a wide range of physical phenomena in diverse solids. The prevailing first-principles approach for EPC, density-functional perturbation theory (DFPT), is computationally demanding and only recently became compatible with the DFT+U corrected DFT approach. Finite-difference methods, as an alternative to DFPT, are less time-consuming and readily compatible with DFT+U as they only require self-consistent calculations. In this work, we present an approximate framework to calculate electron-phonon coupling via finite differences, which incorporates intraband scattering. We validate our methodology through benchmarks against full DFPT calculations and demonstrate its application to cuprate systems.