Possible experimentally observable effects of vertex corrections in superconductors

Abstract

We calculate the effects of vertex corrections, of nonconstant density of states and of a (self-consistently determined) phonon self-energy for the Holstein model on a three-dimensional cubic lattice. We replace vertex corrections with a Coulomb pseudopotential μC* 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 of vertex 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 λ is significantly larger than the bare value. While vertex corrections can cause significant changes in all the above quantities (even when the 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 μC*.

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