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 determined͒ phonon self-energy for the Holstein model on a three-dimensional cubic lattice. We replace vertex corrections with a Coulomb pseudopotential C * adjusted to give the same T c , 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 approximation͒ 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 is significantly larger than the bare value. While vertex corrections can cause significant changes in all the above quantities ͑even when the bare electronphonon coupling is small͒, 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 C * .

Superconducting states of the quasi-2D Holstein model: effects of vertex and non-local corrections

“…For half filling, the Green's function at the van-Hove points is pure imaginary, whereas for the dilute system, it is mostly real, so sums over products of Green's functions can change sign with respect to the Migdal-Eliashberg result. This sign change is also seen in DMFT simulations of the 3D Holstein model [19].…”

Quantitative analysis of nonadiabatic effects in dense H3S and PH3 superconductors

“…The application of the above Eliashberg equations to describe the electron-phonon superconductivity is justified for systems in which the value of the phonon energy scale (Debye frequency, ω D ) to the electron energy scale (Fermi energy, ε F ) ratio is negligible. Otherwise the Eliashberg equations should be generalized by taking into account the lowest-order vertex correction [33][34][35][36][37]: and…”

Electron and phonon dispersions of the two-dimensional Holstein model: effects of vertex and non-local corrections

“…DMFA has been extensively applied to solving infinitedimensional lattice models, where the DMFA formalism becomes exact [15,16]. It has also been used to approximate two and three dimensional systems, where it is known as the local approximation [17,11]. In DMFA, the self-energy is assumed to be local, and Σ(k, z) is replaced by its momentum-independent counterpart, Σ(z).…”

“…In this paper, the perturbation theory shown in figure 2 is used, following directly from the free energy expansion of Baym and Kadanoff [11]. The electron self-energy has two terms, Σ ME (ω, K) neglects vertex corrections (figure 2(a)), and Σ VC (ω, K) corresponds to the vertex corrected case (figure 2(b)).…”