Non-uniform grids to accelerate electron-phonon coupling calculations for superconductivity

Overview & Synopsis

Efficient and accurate evaluation of electron-phonon interactions is essential for predictive superconductivity calculations, but dense Brillouin zone sampling requirements pose a major computational bottleneck. To overcome this, we introduce an accelerated, highly scalable framework that combines a double delta truncation scheme with non-uniform Farey grids in both $\mathbf{k}$ and $\mathbf{q}$ space. The truncation strategy significantly reduces computational cost by restricting integration to states satisfying energy constraints near the Fermi level, while the Farey grids dynamically resolve sampling errors from localized scattering and stabilize convergence. Applied to elemental aluminium and several high-pressure hydrides, this combined methodology reduces computational cost by up to two orders of magnitude and yields electron-phonon coupling constants and superconducting critical temperatures Tc typically within about 5% of full-grid benchmarks. This approach overcomes sampling bottlenecks associated with dense uniform grids, making accurate, low-cost predictions of superconductivity in complex quantum materials feasible.