Uniform electron benchmark for the first-principles $G{W}_0$-Eliashberg theory

Abstract

We investigate the numerical behavior of the Eliashberg equations for phonon-mediated superconductivity, incorporating normal-state self-energy calculations within the consistent $G{W}_0$ approximation. We account for the full wavenumber and frequency dependences of both the screened Coulomb interaction and phonon-mediated attraction. We present results for the prototypical uniform electron gas system with model Einstein phonons at temperatures of a few kelvin. At extremely low temperatures, we efficiently execute the required convolutions of Green's functions and interactions in Matsubara frequency and wavenumber using intermediate representation and Fourier convolution techniques. In particular, we elucidate the interplay between electron-phonon $\omega$-mass and $k$-mass renormalizations of the electronic self-energy in determining the normal-state effective mass, spectral weight and the superconducting transition temperature. The electron density regimes where the plasmon effect enhances or suppresses the phonon-mediated superconductivity on top of the static Coulomb effect are revealed. We compare our comprehensive Eliashberg calculation results with those from density functional theory for superconductors, where the functionals have been constructed with reference to Eliashberg theory. Our model, methods, and results provide a valuable benchmark for first-principles superconducting calculations that treat screened Coulomb interaction effects non-empirically.

11 pages, 6 figures, 2 tables

References in corpus (23)

• The GW method
• Ab-initio theory of superconductivity - I: Density functional formalism and approximate functionals
• Quantum Crystal Structure in the 250 K Superconducting Lanthanum Hydride
• Ab-initio theory of superconductivity - II: Applications to elemental metals
• First-principles study of the pressure and crystal-structure dependences of the superconducting transition temperature in compressed sulfur hydrides
• Compressing Green's function using intermediate representation between imaginary-time and real-frequency domains
• Effect of van Hove singularities on high-Tc superconductivity in H3S
• Sparse sampling approach to efficient ab initio calculations at finite temperature
• Development of Density-Functional Theory for Plasmon-Assisted Superconducting State: Application to Lithium Under High Pressures
• sparse-ir: optimal compression and sparse sampling of many-body propagators
• Ab initio theory of plasmonic superconductivity within the Eliashberg and density-functional formalisms
• Multiband full-bandwidth anisotropic Eliashberg theory of interfacial electron-phonon coupling and high-T${}_c$ superconductivity in FeSe/SrTiO${}_3$
• Anisotropic superconducting gaps in YNi${}_2$B${}_2$C: A first-principles investigation
• Role of Coulomb interaction in the superconducting properties of CaC6 and H under pressure
• Full-bandwidth anisotropic Migdal-Eliashberg theory and its application to superhydrides
• Density Functional Theory for Plasmon-Assisted Superconductivity
• Efficient ab initio many-body calculations based on sparse modeling of Matsubara Green's function
• Efficient ab initio Migdal-Eliashberg calculation considering the retardation effect in phonon-mediated superconductors
• Density Functional Theory for Superconductors with Particle-hole Asymmetric Electronic Structure
• Coulomb interactions and conventional superconductivity: when going beyond the random phase approximation is essential
• Screening Induced Crossover between Phonon- and Plasmon-Mediated Pairing in Layered Superconductors
• Origin of the Coulomb Pseudopotential
• Revisiting the homogeneous electron gas in pursuit of the properly normed ab initio Eliashberg theory