What are the experimentally observable effects of vertex corrections in superconductors?

TL;DR

This study investigates the observable effects of vertex corrections in superconductors, analyzing their impact on thermodynamic properties and distinguishing these effects from Coulomb pseudopotential influences.

Contribution

It provides a detailed calculation of vertex correction effects on superconducting properties, highlighting their unique observable signatures beyond Coulomb pseudopotential effects.

Findings

Vertex corrections significantly alter superconducting parameters.

The isotope coefficient uniquely reveals effects not mimicked by Coulomb pseudopotential.

Dressed electron-phonon coupling lambda is larger than the bare value.

Abstract

We calculate the effects of vertex corrections, of non-constant density of states and of a (self-consistently determined) phonon self-energy for the Holstein model on a 3D cubic lattice. We replace vertex corrections with a Coulomb pseudopotential, mu*, adjusted to give the same Tc, and repeat the calculations, to see which effects are a distinct feature of vertex corrections. This allows us to determine directly observable effects ofvertex corrections on a variety of thermodynamic properties of superconductors. To this end, we employ conserving approximations (in the local approximation) to calculate the superconducting critical temperatures, isotope coefficients, superconducting gaps, free-energy differences and thermodynamic critical fields for a range of parameters. We find that the dressed value of lambda is significantly larger than the bare value. While vertex corrections can cause significant changes in all the above quantities (even whenthe bare electron-phonon coupling is small), the changes can usually be well-modeled by an appropriate Coulomb pseudopotential. The isotope coefficient proves to be the quantity that most clearly shows effects of vertex corrections that can not be mimicked by a mu*.