Competition between electron-phonon attraction and weak Coulomb repulsion

TL;DR

This paper investigates the Holstein-Hubbard model in infinite dimensions, revealing that Coulomb repulsion unexpectedly stabilizes both CDW and superconducting phases, with commensurate CDW being more robust than superconductivity.

Contribution

It challenges conventional beliefs by showing Coulomb repulsion stabilizes both phases and explains the robustness of commensurate CDW through perturbation theory analysis.

Findings

Coulomb repulsion stabilizes both incommensurate CDW and superconducting phases.

Commensurate CDW transition temperature is more robust than superconducting transition temperature.

Perturbation theory explains the surprising stabilization effects.

Abstract

The Holstein-Hubbard model is examined in the limit of infinite dimensions. Conventional folklore states that charge-density-wave (CDW) order is more strongly affected by Coulomb repulsion than superconducting order because of the pseudopotential effect. We find that both incommensurate CDW and superconducting phases are stabilized by the Coulomb repulsion, but, surprisingly, the commensurate CDW transition temperature is more robust than the superconducting transition temperature. This puzzling feature is resolved by a detailed analysis of perturbation theory.