Retardation effects and the Coulomb pseudopotential in the theory of superconductivity

Abstract

In the theory of electron-phonon superconductivity both the magnitude of the electron-phonon coupling $\lambda$ as well as the Coulomb pseudopotential ${\mu }^{\ast }$ are important to determine the transition temperature $T_c$ and other properties. We calculate corrections to the conventional result for the Coulomb pseudopotential. Our calculation are based on the Hubbard-Holstein model, where electron-electron and electron-phonon interactions are local. We develop a perturbation expansion, which accounts for the important renormalization effects for the electrons, the phonons, and the electron-phonon vertex. We show that retardation effects are still operative for higher order corrections, but less efficient due to a reduction of the effective bandwidth. This can lead to larger values of the pseudopotential and reduced values of $T_c$. The conclusions from the perturbative calculations are corroborated up to intermediate couplings by comparison with non-perturbative dynamical mean-field results.

arXiv comment24 pages, 19 figures

References in corpus (22)

• The numerical renormalization group method for quantum impurity systems
• Renormalization Group Approach to Interacting Fermions
• Electron-phonon interactions and related physical properties of metals from linear-response theory
• Real-time dynamics in Quantum Impurity Systems: A Time-dependent Numerical Renormalization Group Approach
• The Challenge of Unconventional Superconductivity
• Ab-initio theory of superconductivity - I: Density functional formalism and approximate functionals
• Sum-rule Conserving Spectral Functions from the Numerical Renormalization Group
• Ab-initio theory of superconductivity - II: Applications to elemental metals
• A Numerical Renormalization Group approach to Green's Functions for Quantum Impurity Models
• Superconductivity in lithium, potassium and aluminium under extreme pressure: A first-principles study
• Numerical Renormalization Group Study of the Anderson-Holstein Impurity Model
• To use or not to use cool superconductors?
• Electronic Correlation effects in superconducting picene from ab-initio calculations
• Electron-phonon vertex in the two-dimensional one-band Hubbard model
• Intercalant and intermolecular phonon assisted superconductivity in K-doped picene
• Competition between electron-phonon attraction and weak Coulomb repulsion
• Quantitative reliability of Migdal-Eliashberg theory for strong electron-phonon coupling
• Vibrational spectrum and electron-phonon coupling of doped solid picene from first principles
• Dynamical mean-field theory and numerical renormalization group study of superconductivity in the attractive Hubbard model
• Retardation effects in the Holstein-Hubbard chain at half-filling
• Phonon-mediated tuning of instabilities in the Hubbard model at half-filling
• Theory of electron-phonon superconductivity: Does retardation really lead to a small Coulomb pseudopotential?

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