Efficient anisotropic Migdal-Eliashberg calculations with the Intermediate Representation basis and Wannier interpolation

Abstract

In this study, we combine the ab initio Migdal-Eliashberg approach with the intermediate representation for the Green's function, enabling accurate and efficient calculations of the momentum-dependent superconducting gap function while fully considering the effect of the Coulomb retardation. Unlike the conventional scheme that relies on a uniform sampling across Matsubara frequencies - demanding hundreds to thousands of points - the intermediate representation works with fewer than 100 sampled Matsubara Green's functions. The developed methodology is applied to investigate the superconducting properties of three representative low-temperature elemental metals: aluminum (Al), lead (Pb), and niobium (Nb). The results demonstrate the power and reliability of our computational technique to accurately solve the ab initio anisotropic Migdal-Eliashberg equations even at extremely low temperatures, below 1 Kelvin.

13 pages, 8 figures

References in corpus (7)

• Quantum ESPRESSO: a modular and open-source software project for quantum simulations of materials
• Advanced capabilities for materials modelling with Quantum ESPRESSO
• Quantum ESPRESSO toward the exascale
• Origin of superconductivity and latent charge density wave in NbS${}_2$
• Experimental demonstration of a two-band superconducting state for lead using scanning tunneling spectroscopy
• $Abinitio$ study of Li-Mg-B superconductors
• Superconducting properties of MoTe${}_2$ from the $abinitio$ anisotropic Migdal-Eliashberg theory

Cited by in corpus (6)

• The Wannier Function Software Ecosystem for Materials Simulations
• Charting the landscape of Bardeen-Cooper-Schrieffer superconductors in experimentally known compounds
• Electron-phonon vertex correction effect in superconducting H3S
• Superconductivity, valence-skipping and topological crystalline metal in AgSnSe${}_2$
• High-$T_{\mathrm{c}}$ Ag${}_x$BC and Cu${}_x$BC superconductors accessible via topochemical reactions
• First-principles evidence for conventional superconductivity in a quasicrystal approximant