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Publié le 14 mars 2023

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1

Cai, J., X. L. Lei et L. M. Xie. « Vertex correction to the Eliashberg equation for the superconducting critical temperature ». Physical Review B 39, no 16 (1 juin 1989) : 11618–23. http://dx.doi.org/10.1103/physrevb.39.11618.

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2

Wu, Hang-Sheng, Zheng-Yu Weng, Guangda Ji et Zi-Fang Zhou. « Analytic solution to the Eliashberg equation for the superconducting critical temperatures ». Journal of Physics and Chemistry of Solids 48, no 5 (janvier 1987) : 395–417. http://dx.doi.org/10.1016/0022-3697(87)90100-4.

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3

Dayan, Moshe. « Large energy gap solutions of the generalized eliashberg equation in high temperature superconductors ». Physica C : Superconductivity 167, no 1-2 (avril 1990) : 228–35. http://dx.doi.org/10.1016/0921-4534(90)90507-b.

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4

BASU, S., SUJIT SARKAR et S. SIL. « PRESSURE COEFFICIENT OF THE SUPERCONDUCTING TRANSITION TEMPERATURE IN THE STRONG COUPLING LIMIT ». Modern Physics Letters B 10, no 18 (10 août 1996) : 839–43. http://dx.doi.org/10.1142/s021798499600095x.

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Pressure coefficient (β) of the superconducting transition temperature (T c ) for a two dimensional system is studied in presence of Coulomb interaction, using Eliashberg equation with the Einstein approximation for the phonon system, within the van Hove scenario. β is found to be high in the low-T c region and low in the high-T c region. β is positive in the underdoped region and becomes negative in the overdoped region. For a given value of Fermi energy, β increases in the underdoped region and decreases in the overdoped region with the increase of Coulomb repulsion.
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5

Zhao, G. L., et D. Bagayoko. « The Gap Function in YBa2Cu3O7 ». International Journal of Modern Physics B 12, no 29n31 (20 décembre 1998) : 3057–62. http://dx.doi.org/10.1142/s0217979298002052.

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We have solved the four-dimensional anisotropic Eliashberg gap equation for YBa2Cu3O7 (YBCO) using the calculated electronic structure and the electron–phonon interaction matrix elements. The calculated T c for YBCO is about 89 K or μ*= 0.1. At or slightly above the transition temperature T c , the real part of the gap function Δ(k, 0), for all the k-points on the Fermi surface, becomes zero and the material is not superconducting. However, the energy gap function Δ(k,ω) is still nonzero for ω > 0 for some electronic states, leading to a pseudo-gap behavior in YBCO.
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6

ZHAO, G. L., et D. BAGAYOKO. « AB-INITIO CALCULATIONS OF SUPERCONDUCTING PROPERTIES OF YBa2Cu3O7 ». International Journal of Modern Physics B 13, no 29n31 (20 décembre 1999) : 3579–81. http://dx.doi.org/10.1142/s0217979299003465.

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We present ab-initio calculations for the electronic structure and superconducting properties of YBa 2 Cu 3 O 7 (YBCO). The electronic structure was calculated using a self-consistent ab-initio LCAO method. We solved the anisotropic Eliashberg gap equation numerically. The strong coupling of the high energy optical phonons around 60-73 meV, with the electrons at the Fermi surface, leads to a high Tc in YBCO. The calculated Tc is about 89 K for μ*=0.1. The good agreement of the calculated results with experimental measurements and the ab-initio nature of the calculations support the scenario of an anisotropic s-wave superconductor for YBCO.
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7

Mineev-Weinstein, M. B. « Exact calculations of Tc from Eliashberg equation for simultaneous action of different channels of pairing ». Physica C : Superconductivity 182, no 4-6 (novembre 1991) : 322–26. http://dx.doi.org/10.1016/0921-4534(91)90529-8.

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8

Feher, Alexander, S. B. Feodosyev, I. A. Gospodarev, V. I. Grishaev, K. V. Kravchenko, E. V. Manzhelii et Eugenyi Syrkin. « Peculiarities of the Electron-Phonon Interaction in Graphite Containing Metallic Intercalated Layers ». Defect and Diffusion Forum 297-301 (avril 2010) : 75–81. http://dx.doi.org/10.4028/www.scientific.net/ddf.297-301.75.

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The calculation of the local density of electronic states of graphene with vacancies, using the method of Jacobi matrix, was performed. It was shown that for atoms in the sublattice with a vacancy the local density of electronic states conserves the Dirac singularity, similarly as in an ideal graphene. A quasi-Dirac singularity was observed also in the phonon spectra of graphite for the atom displacements in the direction perpendicular to layers. Changes of phonon spectra of graphite intercalated with various metals were analyzed. On the basis of our results and using the BCS theory and Eliashberg equation we proposed what dynamic properties an intercalated graphite system should show to obtain an increased Tc.
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9

NISHIO, Yoshimasa, Masafumi SHIRAI, Naoshi SUZUKI et Kazuko MOTIZUKI. « ELECTRON-PHONON INTERACTION, LATTICE DYNAMICS AND SUPERCONDUCTIVITY OF LAYERED TRANSITION-METAL DICHALCOGENIDE NbS2 ». International Journal of Modern Physics B 07, no 01n03 (janvier 1993) : 188–92. http://dx.doi.org/10.1142/s0217979293000421.

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Lattice dynamics of NbX 2( X = S , Se ) is studied by taking account of electron-phonon interaction derived microscopically on the basis of the realistic tight-binding bands fitted to the first-principle bands of NbX 2. Remarkable frequency renormalization of Σ1 phonon mode around [Formula: see text] is caused due to characteristic wave-vector and mode dependences of the electron-phonon interaction as well as nesting effect of Fermi surface. It is also shown that the short range force constant for neighboring X ions on different X-layers in the same X-Nb-X sandwich determines primarily whether lattice instability occurs ( NbSe 2 case) or does not occur ( NbS 2 case). By using the electron-phonon interaction and the lattice dynamics obtained for NbS 2 we have calculated the spectral function α2F(ω) and determined superconducting transition temperature T c by solving the linearlized Eliashberg equation. Renormalization of phonon frequencies due to the eletron-phonon interaction raises considerably the transition temperature and the obtained value of T c agrees in order of magnitude with the experimental data.
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10

Goto, Hiroki, et Yuhei Natsume. « Effects of the Vertex Correction by the Method of Nambu to the Eliashberg-Migdal Equation in the Strong Coupling Superconductivity under the Ultra-High Magnetic Field ». Journal of the Physical Society of Japan 64, no 8 (15 août 1995) : 3031–37. http://dx.doi.org/10.1143/jpsj.64.3031.

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11

Sue, Nobuhiro, et Yuhei Natsume. « Self-Consistent Calculations of Eliashberg Equation for Strong CouplingSuperconductivity with Anisotropic Gap under the Modulation of Two Kinds of Nodal Wavevectors to 2-Dimensional Electronic Bands ». Journal of the Physical Society of Japan 65, no 5 (15 mai 1996) : 1166–69. http://dx.doi.org/10.1143/jpsj.65.1166.

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12

Wysokinski, Karol I. « Eliashberg-type equations for correlated superconductors ». Physical Review B 54, no 5 (1 août 1996) : 3553–61. http://dx.doi.org/10.1103/physrevb.54.3553.

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13

Puig-Puig, L., F. Lopez-Aguilar et J. Costa-Quintana. « Eliashberg equations in strong-correlation systems ». Journal of Physics : Condensed Matter 6, no 26 (27 juin 1994) : 4929–36. http://dx.doi.org/10.1088/0953-8984/6/26/014.

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14

Honerkamp, C., et M. Salmhofer. « Eliashberg Equations Derived from the Functional Renormalization Group ». Progress of Theoretical Physics 113, no 6 (1 juin 2005) : 1145–58. http://dx.doi.org/10.1143/ptp.113.1145.

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15

Fil', D. V., D. O. Livdan et O. I. Tokar'. « Eliashberg equations analogue in Anderson model for HTSC ». Physica C : Superconductivity and its Applications 162-164 (décembre 1989) : 797–98. http://dx.doi.org/10.1016/0921-4534(89)91265-3.

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16

UMMARION, G. A., R. S. GONNELLI, O. V. DOLGOV et S. V. SHULGA. « ELECTRON-PHONON SPECTRAL FUNCTION AND TWO-BAND MODEL IN TUNNELING MEASUREMENTS ON MgB2 ». International Journal of Modern Physics B 17, no 04n06 (10 mars 2003) : 643–48. http://dx.doi.org/10.1142/s0217979203016364.

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In the present work we calculate for the first time the density of states of MgB 2 for different tunneling directions by directly solving the two-band Eliashberg equations in the real-axis formulation starting from the first-principle calculation of the interband and intraband electron-phonon spectral functions. This complicated numeric procedure allows preserving the fine structures of the DOS in the phonon energy range. We show that the numeric inversion of the standard single-band Eliashberg equations when applied to the densities of states obtained by the two-band model may lead to artifacts in the extracted electron-phonon spectral function α2 F(ω). We also suggest that the small DOS structures produced by the two-band inter-action at energies between 20 and 100 meV can be observed only at very low temperature in junctions in perfect clean limit.
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17

Szczęśniak, R. « The Numerical Solution of the Imaginary-Axis Eliashberg Equations ». Acta Physica Polonica A 109, no 2 (février 2006) : 179–86. http://dx.doi.org/10.12693/aphyspola.109.179.

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18

Grimaldi, C., L. Pietronero et S. Strässler. « Nonadiabatic superconductivity. II. Generalized Eliashberg equations beyond Migdal’s theorem ». Physical Review B 52, no 14 (1 octobre 1995) : 10530–46. http://dx.doi.org/10.1103/physrevb.52.10530.

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19

Santi, G., T. Jarlborg, M. Peter et M. Weger. « Existence of boths andd-wave solutions of Eliashberg equations ». Journal of Superconductivity 8, no 4 (août 1995) : 405–8. http://dx.doi.org/10.1007/bf00722816.

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20

Kudryashov, N. A., A. A. Kutukov et E. A. Mazur. « Metal hydrogen sulfide superconducting temperature ». Novel Superconducting Materials 3, no 1 (1 janvier 2017) : 1–5. http://dx.doi.org/10.1515/nsm-2017-0001.

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AbstractÉliashberg theory is generalized to the electronphonon (EP) systems with the not constant density of electronic states. The phonon contribution to the anomalous electron Green’s function (GF) is considered. The generalized Éliashberg equations with the variable density of electronic states are resolved for the hydrogen sulphide SHThe results of the solution of the Eliashberg equations for the Im-3m (170 GPa), Im-3m (200 GPa) and R3m (120 GPa) phases are presented. A peak value T
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21

Norman, M. R. « Solutions of the magnetic Eliashberg equations for heavy-fermion superconductors ». Physical Review B 37, no 10 (1 avril 1988) : 4987–95. http://dx.doi.org/10.1103/physrevb.37.4987.

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22

Malozovsky, Y. M., S. M. Bose, P. Longe et J. D. Fan. « Eliashberg equations and superconductivity in a layered two-dimensional metal ». Physical Review B 48, no 14 (1 octobre 1993) : 10504–13. http://dx.doi.org/10.1103/physrevb.48.10504.

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23

UMMARINO, G. A., R. S. GONNELLI et D. DAGHERO. « ELIASHBERG EQUATIONS AND THE PHENOMENOLOGY OF FIELD-EFFECT-DOPED C60 ». International Journal of Modern Physics B 16, no 11n12 (20 mai 2002) : 1539–46. http://dx.doi.org/10.1142/s0217979202011123.

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In a recent paper [J. H. Schön, Ch. Kloc, R. C. Haddon and B. Batlogg, Nature408, 549 (2000)] C 60 doped with holes by application of an intense electric field was found to superconduct at remarkably high temperature. In this paper we show that the observed dependence of T c on doping can be reproduced by solving the (four) s-wave Eliashberg equations in the case of a finite, non-half-filled energy band, with the only initial hypothesis that the Coulomb pseudopotential depends on the filling in a very simple and plausible way. The experimental data are reproduced by using very reasonable values of the physical parameters involved. We also show that the application of the same approach to new experimental data [ J. H. Schön, Ch. Kloc and B. Batlogg, Science293, 2432 (2001)] also gives good results.
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24

Schneider, Rudolf, Jochen Geerk, Alexander G. Zaitsev, Rolf Heid, K. P. Bohnen et H. von Löhneysen. « Interband Pairing Interaction in Magnesium Diboride Probed by Tunneling Spectroscopy ». Advances in Science and Technology 47 (octobre 2006) : 69–74. http://dx.doi.org/10.4028/www.scientific.net/ast.47.69.

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We report on the study of the interband pairing interaction in the two-band superconductor MgB2 by tunneling spectroscopy using thin film tunnel junctions. The films were deposited in situ by an approach comprising a conventional planar B sputter gun and a special homemade Mg evaporator providing a high vapor pressure. For the tunneling experiments sandwich-type crossed-strip tunnel junctions with a native MgB2 oxide as the potential barrier and Al, In or Pb counterelectrodes were prepared. Voltage-dependent differential conductance measurements revealed estimates of the barrier thickness and height of 1.5 nm and 1.6 eV, respectively, and allowed us to determine the phonon-induced structures in the tunneling density of states of the phonon-mediated superconductor MgB2. The analysis of the reduced density of states using the standard single-band Eliashberg equations yielded an effective electron-phonon spectral function accounting for the smaller energy gap. A further analysis involving ab-initio LDA calculations and the two-band Eliashberg equations revealed that the dominant feature in the effective spectral function, a strong peak at 58 meV, was mainly due to the interband pairing interaction.
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25

Szczȩs̀niak, R. « The thermodynamic properties of the superconductor : The two-band Eliashberg equations ». Solid State Communications 145, no 3 (janvier 2008) : 137–42. http://dx.doi.org/10.1016/j.ssc.2007.10.010.

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26

Ummarino, G. A., et R. S. Gonnelli. « s- and d-wave solution of Eliashberg equations with finite bandwidth ». Physica C : Superconductivity 341-348 (novembre 2000) : 295–96. http://dx.doi.org/10.1016/s0921-4534(00)00487-1.

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27

Norman, M. R. « Solutions of the magnetic Eliashberg equations for heavy fermion superconductors (abstract) ». Journal of Applied Physics 63, no 8 (15 avril 1988) : 3903. http://dx.doi.org/10.1063/1.340600.

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28

Xiong, Shi-jie. « Eliashberg Equations and Coulomb Pseudopotential for Superconductivity via Sign-Opposite Interactions ». Communications in Theoretical Physics 14, no 2 (septembre 1990) : 203–8. http://dx.doi.org/10.1088/0253-6102/14/2/203.

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29

Santi, Gilles, Thomas Jarlborg, Martin Peter et Meir Weger. « Solutions of the Eliashberg equations for models of electron-phonon coupling ». Czechoslovak Journal of Physics 46, S2 (février 1996) : 919–20. http://dx.doi.org/10.1007/bf02583767.

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30

Dayan, Moshe. « A generalization of the isotropic Eliashberg equations to high temperature superconductors ». Solid State Communications 76, no 10 (décembre 1990) : 1215–19. http://dx.doi.org/10.1016/0038-1098(90)90063-h.

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31

Ummarino, Giovanni A., Renato S. Gonnelli et Dario Daghero. « REAL-AXIS SOLUTION OF ELIASHBERG EQUATIONS IN VARIOUS ORDER-PARAMETER SYMMETRIES AND TUNNELING CONDUCTANCE OF OPTIMALLY-DOPED HTSC ». International Journal of Modern Physics B 14, no 25n27 (30 octobre 2000) : 2944–49. http://dx.doi.org/10.1142/s0217979200003149.

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In the present work we calculate the theoretical tunneling conductance curves of SIN junctions involving high-T c superconductors, for different possible symmetries of the order parameter (s, d, s + i d, s + d, anisotropics and extendeds). To do so, we solve the real-axis Eliashberg equations in the case of an half-filled infinite band. We show that some of the peculiar characteristics of HTSC tunneling curves (dip and hump at eV > Δ, broadening of the gap peak, zero bias and so on) can be explained in the framework of the Migdal-Eliashberg theory. The theoretical d I/ d V curves calculated for the different symmetries at T=4 K are then compared to various experimental tunneling data obtained in optimally-doped BSCCO, TBCO, HBCO, LSCO and YBCO single crystals. To best fit the experimental data, the scattering by non-magnetic impurities has to be taken into account, thus limiting the sensitivity of this procedure in determining the exact gap symmetry of these materials. Finally, the effect of the temperature on the theoretical tunneling conductance is also discussed and the curves obtained at T = 2 K are compared to those given by the analytical continuation of the imaginary-axis solution.
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32

Ummarino, Giovanni Alberto. « Eliashberg Theory of a Multiband Non-Phononic Spin Glass Superconductor ». Magnetochemistry 6, no 4 (16 octobre 2020) : 51. http://dx.doi.org/10.3390/magnetochemistry6040051.

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I solved the Eliashberg equations for a multiband non-phononic s± wave spin-glass superconductor, calculating the temperature dependence of the gaps and of superfluid density. Their behaviors were revealed to be unusual: showing non-monotonic temperature dependence and reentrant superconductivity. By considering particular input parameters values that could describe the iron pnictide EuFe2(As1−xPx)2, a rich and complex phase diagram arises, with two different ranges of temperature in which superconductivity appears.
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33

KUZEMSKY, A. L. « TWO-COMPONENT ALLOY MODEL FOR BISMUTHATE CERAMICS ». Modern Physics Letters B 10, no 14 (20 juin 1996) : 627–33. http://dx.doi.org/10.1142/s0217984996000699.

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The disordered binary substitutional A 1−x B x alloy model has been proposed for the description of the normal and superconducting properties of bismuthate ceramics Ba(Pb,Bi)O 3. The Eliashberg-type equations for the strong coupling superconductivity in strongly disordered alloys have been used to describe the superconducting properties. The relevant configurational averaging has been performed in the framework of CPA. The concentration dependence of electron-phonon coupling constant λ(x) and transition temperature Tc(x) has been calculated.
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34

Barbiellini, B., M. Weger et M. Peter. « Solutions of Eliashberg equations for an electron-phonon coupling with a cutoff ». Physica C : Superconductivity 235-240 (décembre 1994) : 2397–98. http://dx.doi.org/10.1016/0921-4534(94)92419-8.

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35

Santi, G., T. Jarlborg, M. Peter et M. Weger. « s- and d-wave symmetries of the solutions of the Eliashberg equations ». Physica C : Superconductivity 259, no 3-4 (mars 1996) : 253–64. http://dx.doi.org/10.1016/0921-4534(96)00052-4.

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36

Weger, M., B. Barbiellini et M. Peter. « Solutions of Eliashberg equations for an electron-phonon coupling with a cutoff ». Zeitschrift f�r Physik B Condensed Matter 94, no 4 (décembre 1994) : 387–93. http://dx.doi.org/10.1007/bf01317400.

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37

Holcomb, M. J. « Finite-temperature real-energy-axis solutions of the isotropic Eliashberg integral equations ». Physical Review B 54, no 9 (1 septembre 1996) : 6648–60. http://dx.doi.org/10.1103/physrevb.54.6648.

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38

Karakozov, A. E., E. G. Maksimov et A. A. Mikhailovsky. « The investigation of Eliashberg equations for superconductors with strong electron-phonon interaction ». Solid State Communications 79, no 4 (juillet 1991) : 329–35. http://dx.doi.org/10.1016/0038-1098(91)90556-b.

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39

Mierzejewski, M., J. Zieliński et P. Entel. « Eliashberg equations with momentum-dependent Kernels for the two-dimensional Hubbard model ». Journal of Superconductivity 9, no 1 (février 1996) : 81–87. http://dx.doi.org/10.1007/bf00728430.

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40

Ashraf, M., et J. P. Carbotte. « On different formulas for the Tc of an impure anisotropic superconductor ». Canadian Journal of Physics 63, no 5 (1 mai 1985) : 574–85. http://dx.doi.org/10.1139/p85-090.

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Exact numerical solutions of the Eliashberg equations are obtained for several representative metals, from which the impurity dependence of the critical temperature of an anisotropic superconductor is determined. The exact results are used to assess the accuracy of some of the simple, approximate, but analytic, formulas now available in the literature. All are found to be, at best, semiquantitative. An attempt is made to improve on the available formulas by deriving a new one based on the original quantitative work of Leavens and Carbotte for pure metals. While our final analytic formula should be useful for many purposes, it is still found that for accurate quantitative work the full equations are preferable.
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41

Mukhin, Sergei. « Euclidean Q-Balls of Fluctuating SDW/CDW in the ‘Nested’ Hubbard Model of High-Tc Superconductors as the Origin of Pseudogap and Superconducting Behaviors ». Condensed Matter 7, no 2 (31 mars 2022) : 31. http://dx.doi.org/10.3390/condmat7020031.

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The origin of the pseudogap and superconducting behaviors in high-Tc superconductors is proposed, based on the picture of Euclidean Q-balls formation that carry Cooper/local-pair condensates inside their volumes. Euclidean Q-balls that describe bubbles of collective spin-/charge density fluctuations (SDW/CDW) oscillating in Matsubara time are found as a new self-consistent solution of the Eliashberg equations in the ‘nested’ repulsive Hubbard model of high-Tc superconductors. The Q-balls arise due to global invariance of the effective theory under the phase rotation of the Fourier amplitudes of SDW/CDW fluctuations, leading to conservation of the ‘Noether charge’ Q in Matsubara time. Due to self-consistently arising local minimum of their potential energy at finite amplitude of the density fluctuations, the Q-balls provide greater binding energy of fermions into local/Cooper pairs relative to the usual Frohlich mechanism of exchange with infinitesimal lattice/charge/spin quasiparticles. We show that around some temperature T* the Q-balls arise with a finite density of superconducting condensate inside them. The Q-balls expand their sizes to infinity at superconducting transition temperature Tc. The fermionic spectral gap inside the Q-balls arises in the vicinity of the ‘nested’ regions of the bare Fermi surface. Solutions are found analytically from the Eliashberg equations with the ‘nesting’ wave vectors connecting ‘hot spots’ in the Brillouin zone. The experimental ‘Uemura plot’ of the linear dependence of Tc on superconducting density ns in high-Tc superconducting compounds follows naturally from the proposed theory.
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42

Ummarino, G. A., R. S. Gonnelli, S. Massidda et A. Bianconi. « Two-band Eliashberg equations and the experimental Tc of the diboride Mg1−xAlxB2 ». Physica C : Superconductivity 407, no 3-4 (août 2004) : 121–27. http://dx.doi.org/10.1016/j.physc.2004.05.009.

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43

Drzazga, E. A., I. A. Domagalska, M. W. Jarosik, R. Szczȩśniak et J. K. Kalaga. « Characteristics of Superconducting State in Vanadium : the Eliashberg Equations and Semi-analytical Formulas ». Journal of Superconductivity and Novel Magnetism 31, no 4 (25 août 2017) : 1029–34. http://dx.doi.org/10.1007/s10948-017-4295-y.

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44

Sadovskii, M. V. « Superconducting Transition Temperature for Very Strong Coupling in the Antiadiabatic Limit of Eliashberg Equations ». JETP Letters 113, no 9 (26 avril 2021) : 581–85. http://dx.doi.org/10.1134/s0021364021090034.

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45

Combescot, R. « Critical temperature of superconductors : Exact solution from Eliashberg equations on the weak-coupling side ». Physical Review B 42, no 13 (1 novembre 1990) : 7810–24. http://dx.doi.org/10.1103/physrevb.42.7810.

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46

Livdan, D. O., V. P. Seminozhenko, V. L. Sobolev, O. I. Tokar et D. V. Fil. « An equivalent of the Eliashberg equations in the Anderson model of high-Tc superconductivity ». Physica C : Superconductivity 167, no 5-6 (mai 1990) : 538–48. http://dx.doi.org/10.1016/0921-4534(90)90672-2.

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47

Barbiellini, B., M. Peter et M. Weger. « Solutions of the Eliashberg equations with abnormally large values of 2?(0)/T C ». Journal of Superconductivity 9, no 1 (février 1996) : 59–64. http://dx.doi.org/10.1007/bf00728426.

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48

Wrona, I. A., M. Kostrzewa, K. A. Krok, A. P. Durajski et R. Szczȩśniak. « Carbonaceous sulfur hydride system : The strong-coupled room-temperature superconductor with a low value of Ginzburg–Landau parameter ». Journal of Applied Physics 131, no 11 (21 mars 2022) : 113901. http://dx.doi.org/10.1063/5.0081918.

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The superconducting state in a carbonaceous sulfur hydride (C–S–H) system is probably characterized by the record-high critical temperature of 288 K ([Formula: see text] GPa). We determined the properties of the C–S–H superconducting phase within the scope of both classical Eliashberg equations and the Eliashberg equations with vertex corrections. We took into account the scenarios pertinent to either the intermediate or the high value of an electron–phonon coupling constant ([Formula: see text] or [Formula: see text], respectively). The scenario for the intermediate value, however, cannot be actually realized due to the anomalously high value of the logarithmic phonon frequency ([Formula: see text] K) it would require. On the other hand, we found it possible to reproduce correctly the value of [Formula: see text] and other thermodynamic quantities in the case of strong coupling, with all the reservations discussed in the presented paper. The vertex corrections lower the order parameter values within the range from [Formula: see text]50 K to [Formula: see text]275 K. For the upper critical field [Formula: see text] T, the Ginzburg–Landau parameter [Formula: see text] is of the order of [Formula: see text]. The strong-coupling scenario for the C–S–H system is also suggested by the high values of [Formula: see text] estimated for [Formula: see text] ([Formula: see text], [Formula: see text]), [Formula: see text] ([Formula: see text]–[Formula: see text], [Formula: see text]), and [Formula: see text] ([Formula: see text], [Formula: see text]) compounds. In the case of the C–S–H system, we also anticipate the presence of the antiferromagnetic state above the superconducting state like in the dense [Formula: see text] superconductor. For [Formula: see text] GPa and [Formula: see text] K, the magnetic ordering transition occurs at [Formula: see text] K.
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49

Golubov, A. A. « THERMODYNAMIC CHARACTERISTICS OF Y–Ba–Cu–O TYPE COMPOUNDS IN THE MODEL OF STRONG ELECTRON–PHONON COUPLING ». International Journal of Modern Physics B 02, no 05 (octobre 1988) : 837–45. http://dx.doi.org/10.1142/s0217979288000652.

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Based on recently measured phonon density of states of Y–Ba–Cu–O an investigation of the strong electron-phonon coupling model is carried out. The numerical solutions of the real axis Eliashberg equations are obtained for a number of phonon spectra parameters. Isotope shifts of T c , spectral behavior of the pairing energy Δ(ω) and the ratio 2Δ g / T c (where Δ g is the gap edge) are calculated. The model gives a very small oxygen isotope shift for rather moderate values of the electron-phonon coupling constant λ ~ 3. The results strongly suggest the weak coupling with high frequency phonon modes and strong coupling with low frequency modes.
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50

Zemła, Tomasz P., Klaudia M. Szczȩśniak, Adam Z. Kaczmarek et Svitlana V. Turchuk. « Characterization of the superconducting phase in tellurium hydride at high pressure ». Modern Physics Letters B 33, no 16 (6 juin 2019) : 1950169. http://dx.doi.org/10.1142/s0217984919501690.

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At present, hydrogen-based compounds constitute one of the most promising classes of materials for applications as phonon-mediated high-temperature superconductors. Herein, the behavior of the superconducting phase in tellurium hydride (HTe) at high pressure (p = 300 GPa) is analyzed in detail, by using the isotropic Migdal–Eliashberg equations. The chosen pressure conditions are considered here as a case study which corresponds to the highest critical temperature value [Formula: see text] in the analyzed material, as determined within recent density functional theory simulations. It is found that the Migdal–Eliashberg formalism, which constitutes a strong-coupling generalization of the Bardeen–Cooper–Schrieffer (BCS) theory, predicts that the critical temperature value ([Formula: see text] K) is higher than previous estimates of the McMillan formula. Further investigations show that the characteristic dimensionless ratios for the thermodynamic critical field, the specific heat for the superconducting state, and the superconducting band gap exceed the limits of the BCS theory. In this context, also the effective electron mass is not equal to the bare electron mass as provided by the BCS theory. On the basis of these findings it is predicted that the strong-coupling and retardation effects play pivotal role in the superconducting phase of HTe at 300 GPa, in agreement with similar theoretical estimates for the sibling hydrogen and hydrogen-based compounds. Hence, it is suggested that the superconducting state in HTe cannot be properly described within the mean-field picture of the BCS theory.
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