The electron-phonon theory of superconductors: Tc map and vertex correction

TL;DR

This paper employs an advanced Eliashberg theory with vertex corrections to map superconducting transition temperatures, revealing crossover behaviors and explaining the Tc variations in cuprates through electron-phonon and Coulomb interactions.

Contribution

It introduces a comprehensive Tc mapping approach incorporating vertex and Coulomb corrections, elucidating the mechanisms behind high-Tc superconductivity and its material dependencies.

Findings

Vertex correction and Coulomb interaction lower Tc to experimental levels.

Crossover from weak to strong coupling regimes identified.

Non-adiabatic effects hinder high Tc in light-atom compounds.

Abstract

The strong coupling Eliashberg theory plus vertex correction is used to calculate maps of transition temperature (Tc) in parameter-space characterizing superconductivity. Based on these Tc maps, crossover behaviors are found when electron-phonon interaction increases from weak-coupling region to strong coupling region. Especially, the combined interaction of vertex correction and Coulomb interaction can efficiently depress Tc from extremely high values in standard strong-coupling theory to reasonable values found in experiments and successfully explain the doing-dependent Tc of cuprate superconductors. The strong non-adiabatic effect is the barrier for high-Tc in compounds with compositions of light atoms and with high phonon frequencies.