Tunneling in proximity junctions with paramagnons

Zarate, H. G.; Ćarbotte, J. P.

doi:10.1016/0378-4363(85)90467-x

Cited by 7 publications

(10 citation statements)

References 17 publications

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“…In this case we have to solve four coupled equations for the gaps ∆ s,b (iω n ) and the renormalization functions Z s,b (iω n ), where ω n are the Matsubara frequencies. The imaginaryaxis equations with proximity effect [37][38][39][40][41] are:…”

Section: Model: Proximity Eliashberg Equationsmentioning

confidence: 99%

Proximity Eliashberg theory of electrostatic field-effect doping in superconducting films

et al. 2017

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We calculate the effect of a static electric field on the critical temperature of a s-wave one band superconductor in the framework of proximity effect Eliashberg theory. In the weak electrostatic field limit the theory has no free parameters while, in general, the only free parameter is the thickness of the surface layer where the electric field acts. We conclude that the best situation for increasing the critical temperature is to have a very thin film of a superconducting material with a strong increase of electron-phonon (boson) constant upon charging.

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Section: Model: Proximity Eliashberg Equationsmentioning

confidence: 99%

Proximity Eliashberg theory of electrostatic field-effect doping in superconducting films

et al. 2017

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“…The model we use calculates the critical temperature of the system by solving the one-band s-wave generalized Eliashberg equations [32,33] with proximity effect. Assuming a nearly ideal interface between the surface and bulk layers (jtj 2 ¼ 1, Piatti et al [3] ), four coupled equations for the renormalization functions Z s,b ðiω n Þ and gaps Δ s,b ðiω n Þ on the imaginary axis have to be solved [34][35][36][37][38]…”

Section: Model: Proximity Eliashberg Equationsmentioning

confidence: 99%

“…The model we use calculates the critical temperature of the system by solving the one‐band s‐wave generalized Eliashberg equations with proximity effect. Assuming a nearly ideal interface between the surface and bulk layers (

false| t |^{2} = 1

, Piatti et al), four coupled equations for the renormalization functions

Z_{normals, normalb} false(i ω_{n} false)

and gaps

Δ_{normals, normalb} false(i ω_{n} false)

on the imaginary axis have to be solved

\begin{matrix} ω_{normaln} Z_{normalb} (i ω_{normaln}) = ω_{normaln} + π T \sum_{normalm} Λ_{normalb}^{Z} (i ω_{normaln}, i ω_{normalm}) N_{normalb}^{Z} (i ω_{normalm}) + {normalΓ}_{normalb} N_{normals}^{Z} (i ω_{normaln}) \end{matrix}

\begin{matrix} left \\ Z_{normalb} (i ω_{normaln}) Δ_{normalb} (i ω_{normaln}) = & π T \sum_{normalm} [Λ_{normalb}^{Δ} (i ω_{normaln}, i ω_{normalm}) - μ_{normalb}^{*} (ω_{normalc})] \\ \times Θ (ω_{normalc} - | ω_{normalm} |) N_{normalb}^{Δ} (i ω_{normalm}) + {normalΓ}_{normalb} N_{normals}^{Δ} (i ω_{normaln}) \end{matrix}

…”

Section: Model: Proximity Eliashberg Equationsmentioning

confidence: 99%

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Theoretical Explanation of Electric Field‐Induced Superconductive Critical Temperature Shifts in Indium Thin Films

Ummarino

Romanin

2020

Physica Status Solidi (b)

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Herein, ab initio density functional theory computations and the self‐consistent solution of one‐band s‐wave generalized Eliashberg equations with proximity effect are combined to explain 60 years old experimental data on how a static electric field can affect the superconductive critical temperature of indium thin films. Although electronic densities of states, Fermi energy shifts, and Eliashberg spectral functions can be computed ab initio, the only parameter in the theory that cannot be determined a priori is the thickness of the surface layer affected by the electric field. However, it is shown that in the weak electrostatic field limit, Thomas–Fermi approximation is valid and, therefore, no free parameters are left, as this perturbed layer is known to have a thickness of the order of the Thomas–Fermi screening length. Moreover, it is shown that the theoretical model can reproduce experimental data, even when the magnitudes of the induced charge densities are so small to be usually neglected.

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“…In this case four coupled equations for the gaps ∆ S(N ) (iω n ) and renormalization functions Z S(N ) (iω n ) have to be solved (here S and N indicate "superconductor" and "normal" respectively and ω n denotes the Matsubara frequencies). The Eliashberg equations with proximity effect on the imaginary-axis [3,7,8,9,10,11] are:…”

Section: Model: Proximity Eliashberg Equationsmentioning

confidence: 99%

Superconductive critical temperature of Pb/Ag heterostructures

Ummarino

2020

Physica C: Superconductivity and its Applications

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Recent experimental data (H. Nam et al., Phys. Rev. B 100, 094512 (2019)) of critical temperature and gaps measured on superconductor/normal metal heterostructure (P b/Ag), epitaxially grown, shown a interesting not usual behaviour. The critical temperature decreases strongly but, despite the large differences in the lattice constants and electronic densities of states in the separate components, this heterostructure shows a spatially constant superconducting gap. In the paper it is demonstrated that the proximity Eliashberg equations, whit no free parameters, cannot explain the dependence of critical temperature from the rate d P b /d Ag . However it is sufficient to assume that the density of states at the Fermi level of silver is equal to that of lead in a layer adjacent to the separation interface, presumably of a thickness less than the coherence length of the lead, to perfectly explain the decrease in the critical temperature and the gap value in function of the rate d P b /d Ag always without free parameters. arXiv:1910.13842v1 [cond-mat.supr-con]

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Tunneling in proximity junctions with paramagnons

Cited by 7 publications

References 17 publications

Proximity Eliashberg theory of electrostatic field-effect doping in superconducting films

Proximity Eliashberg theory of electrostatic field-effect doping in superconducting films

Theoretical Explanation of Electric Field‐Induced Superconductive Critical Temperature Shifts in Indium Thin Films

Superconductive critical temperature of Pb/Ag heterostructures

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