EPW: Electron-phonon coupling, transport and superconducting properties using maximally localized Wannier functions

Abstract: The EPW (Electron-Phonon coupling using Wannier functions) software is a Fortran90 code that uses density-functional perturbation theory and maximally localized Wannier functions for computing electron-phonon couplings and related properties in solids accurately and efficiently. The EPW v4 program can be used to compute electron and phonon self-energies, linewidths, electron-phonon scattering rates, electron-phonon coupling strengths, transport spectral functions, electronic velocities, resistivity, anisotropic superconducting gaps and spectral functions within the Migdal-Eliashberg theory. The code now supports spin-orbit coupling, time-reversal symmetry in non-centrosymmetric crystals, polar materials, and $\mathbf{k}$ and $\mathbf{q}$-point parallelization. Considerable effort was dedicated to optimization and parallelization, achieving almost a ten times speedup with respect to previous releases. A computer test farm was implemented to ensure stability and portability of the code on the most popular compilers and architectures. Since April 2016, version 4 of the EPW code is fully integrated in and distributed with the Quantum ESPRESSO package, and can be downloaded through QE-forge at http://qe-forge.org/gf/project/q-e.

• The paper presents EPW, a tool that computes electron-phonon interactions and superconducting properties using DFPT and maximally localized Wannier functions.
• It details enhanced integration with Quantum ESPRESSO, extended support for spin-orbit coupling, and optimization strategies that yield nearly tenfold speedups.
• The study demonstrates EPW's applicability through modeling superconductors, polar materials, and carrier transport phenomena in various test cases.

Overview of "EPW: Electron-phonon coupling, transport and superconducting properties using maximally localized Wannier functions"

The paper introduces the EPW software, a sophisticated tool designed to compute electron-phonon interactions and related properties with high precision and efficiency. Built on the foundation of density-functional perturbation theory (DFPT) and maximally localized Wannier functions (MLWFs), EPW is a robust Fortran90 code that integrates seamlessly with the Quantum ESPRESSO package. The software excels in calculating electron and phonon self-energies, electron-phonon scattering rates, transport spectral functions, and resistivity, among others. It also facilitates the examination of superconducting properties within the Migdal-Eliashberg framework. A significant effort has been made to optimize and parallelize the code, achieving considerable computational speedups.

Key Features and Enhancements

Version 4 of the EPW software, discussed in this paper, brings several enhancements:

• Integration with Quantum ESPRESSO: EPW is fully embedded within Quantum ESPRESSO, streamlining its installation and updating process.
• Extended Functionalities: New support has been added for spin-orbit coupling, handling non-centrosymmetric crystals via time-reversal symmetry, and improved treatment of polar materials for better capturing long-wavelength singularities.
• Optimization and Parallelization: The software was optimized to boost performance, nearly a tenfold speedup compared to previous releases. Parallel computation capabilities have been enhanced, leveraging $\mathbf{k}$ and $\mathbf{q}$-point parallelization.
• Stability Assurance: A comprehensive test farm ensures the software’s stability and compatibility across various compilers and architectures.

Computational Capabilities

The EPW software can:

• Compute electron phonon linewidths and self-energies.
• Evaluate electron-phonon coupling strengths, essential for understanding material conductivity and superconductivity.
• Model anisotropic superconductivity using the Migdal-Eliashberg theory.
• Calculate the Allen-Dynes superconductivity critical temperature.

The use of MLWFs allows EPW to precisely interpolate electron-phonon matrix elements across fine grids of the Brillouin Zone (BZ), which is computationally challenging with standard methods.

Implications and Future Directions

The EPW software opens new possibilities for accurately modeling complex materials, such as superconductors and polar semiconductors. Its enhancements in speed and functionality make it a valuable tool for researchers exploring electron-phonon interactions and their implications on material properties. Looking forward, potential developments could include further parallelization for massively parallel architectures, improved handling of coulomb interactions in superconductors, and extensions to capture electronic transport coefficients more precisely.

Applications and Research Examples

The paper illustrates the capability of EPW through several examples:

• Analysis of heavily-doped B-diamond’s spectral functions.
• Scattering rates in undoped Si, critical for assessing carrier mobilities accurately.
• Investigation of Pb’s electronic resistivity and spectral functions, with and without spin-orbit coupling, showcasing SOC's role in material properties.
• Polar GaN demonstrates EPW's handling of long-range interactions in polar materials.
• Superconductivity in MgB$_2$, emphasizing EPW’s ability to model multi-gap superconductors.

These examples demonstrate EPW’s effectiveness in various research challenges, cementing its role as an indispensable tool for computational materials science.