Nonadiabatic electron–phonon effects in low carrier density superconductors

Cappelluti, E.; Pietronero, L.

doi:10.1002/pssb.200404958

Cited by 11 publications

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“…el−ph ≃ 1.7 − 1.9. Moreover, it was pointed out by Cappelluti et al [2] that nonadiabatic character can be further enhanced by low charge carrier density, that is the case for ZrB 12 [4,5].…”

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confidence: 98%

Anomalous electron-phonon coupling probed on the surface of superconductorZrB12

et al. 2005

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Magnetization measurements under hydrostatic pressure up to 10.5 kbar in zirconium dodecaboride ZrB12 superconductor (Tc ≃ 6.0 K at p = 0) were carried out. A negative pressure effect on Tc with dTc/dp = −0.0225(3) K/kbar was observed. The electron-phonon coupling constant λ el−ph decreases with increasing pressure with d ln λ el−ph /dp ≃ −0.20%/kbar. The magnetic field penetration depth λ was studied in the Meissner state and, therefore, probes only the surface of the sample. The absolute values of λ and the superconducting energy gap at ambient pressure and zero temperature were found to be λ(0) =140(30) nm and ∆0 =1.251(9) meV, respectively. ∆0 scales linearly with Tc as 2∆0/kBTc = 4.79(1). The studies of the pressure effect on λ reveal that λ −2 increases with pressure with d ln λ −2 (0)/dp = 0.60(23) %/kbar. This effect can not be explained within the framework of conventional adiabatic electron-phonon pairing, suggesting that close to the surface, an unconventional non-adiabatic character of the electron-phonon coupling takes place.PACS numbers: 74.70. Ad, 74.62.Fj, 74.25.Ha, 83.80.Fg The traditional concept of superconductivity is strictly associated with the electron-phonon interaction. The conventional theory is based on the Migdal-Eliashberg adiabatic approximation [1] that, in fact, leads to the prediction of many peculiar features which are a direct evidence of a phonon mediated superconductivity. The adiabatic approximation is valid if the parameter ω 0 /E f is small (ω 0 is the relevant phonon frequency and E f is the Fermi energy). Usually this parameter is regarded as a measure of nonadibaticity. However, crossover from a conventional adiabatic to an unconventional nonadiabatic regime does not depend only on the value of the ω 0 /E f ratio. Paci et al. [8] show that even in a case of small "adiabatic" ratio one would expect the nonadiabatic coupling in superconductors having high value of the electron-phonon coupling constant λ el−ph . Among BCS superconductors the zirconium dodecaboride (ZrB 12 ) is probably a candidate for the observation of such type of anomalous coupling. It stems from the rather small value of the Fermi energy ∼1 eV [3] that, together with the Debye temperature ∼20 meV [4], leads to a ratio ω 0 /E f ∼0.02. A strong coupling ratio 2∆/k B T c ≃ 4.8 was observed by surface sensitive techniques [3,6]. This suggests that the electron-phonon coupling constant, which has a bulk value λ el−ph ≃ 0.67 [3], increases at the surface. From the comparison with strong coupled metallic superconductors [7] one would expect λ surf.el−ph ≃ 1.7 − 1.9. Moreover, it was pointed out by Cappelluti et al.[2] that nonadiabatic character can be further enhanced by low charge carrier density, that is the case for ZrB 12 [4,5].One of the key feature of nonadiabatic superconductivity is the observation of unconventional isotope and pressure effects on the magnetic field penetration depth λ. Note, that in adiabatic superconductors (or in the superconductors where the nonadiabatic effects are small) the...

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Anomalous electron-phonon coupling probed on the surface of superconductorZrB12

et al. 2005

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“…We performed calculations of the phonon spectral functions at different temperatures (Eqs. [2][3][4][5] for both excitation wavelengths. The results obtained (Fig.…”

Section: B Group IV Metals -Zirconium and Titaniummentioning

confidence: 99%

“…This may increase the superconducting transition temperature T c in correlated electron systems 3 . In the past years it has been proposed [4][5][6] that nonadiabatic effects in electron-phonon interaction could be responsible for the high-temperature superconductivity in compounds with low carrier density such as fullerenes 7 or MgB 2 8 . The recent measurement of Raman spectra in graphite intercalation compounds 9,10 showed that the phonon frequencies related to in-plane carbon vibrations are significantly larger than those obtained from density functional theory (DFT) calculations in the adiabatic approximation.…”

Section: Introductionmentioning

confidence: 99%

Raman evidence for nonadiabatic effects in optical phonon self-energies of transition metals

Ponosov

Streltsov

2016

Phys. Rev. B

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We report a Raman study of the effect of temperature on the self-energies of optical phonons in a number of transition metals with hexagonal-close-packed structure. Anisotropic softening of phonon energies and narrowing of phonon linewidths with increasing temperature are observed. These effects are reproduced in the calculations of phonon spectral functions based on ab initio electronic structures and with carrier scattering by phonons taken into account. The combined observations and results of simulations indicate a relation between observed anomalies and the renormalization of the electron spectrum due to electron-phonon interaction. It is emphasized that the temperature dependence of the phonon energies resembles anharmonic behavior but is actually an electron-induced effect.

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“…In regards with the nonadiabatic features, fullerides represent a very important test since, due to the extremely high frequencies of the intra-molecular phonon spectrum and to the weak inter-molecular electron hopping [74][75][76], the nonadiabatic ratio w ph /E F is significantly large, w ph /E F 0.4-0.8 [74,75]. On the other hand, in cuprates the two-dimensional character of the electronic band and the closeness of the Fermi level to a logarithmic Van Hove singularity [77] permit to investigate additional nonadiabatic effects triggered by the flatness of the electronic bands near the Van Hove saddle point.…”

Section: Nonadiabatic Superconductivity In Fullerides and Cupratesmentioning

confidence: 99%

Nonadiabatic breakdown and pairing in high-Tc compounds

Pietronero

Cappelluti

2006

Low Temperature Physics

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The electron-phonon interaction plays a fundamental role in the superconducting and normal-state properties of all the high-Tc materials, from cuprates to fullerenes. Another common element of these compounds is in addition the extremely small Fermi energy EF, which is comparable with the range ωph of the phonon frequencies. In such a situation the adiabatic principle ωph/EF⪡1, on which the standard theory of the electron-phonon interaction and of the superconductivity relies, breaks down. In this contribution we discuss the physical consequences of the breakdown of the adiabatic assumption, with special interest on the superconducting properties. We review the microscopic derivation of the nonadiabatic theory of the electron-phonon coupling which explicitly takes into account higher-order electron-phonon scattering not included in the conventional picture. Within this context we discuss also the role of the repulsive electron-electron correlation and the specific phenomenology of cuprates and fullerides

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Nonadiabatic electron–phonon effects in low carrier density superconductors

Cited by 11 publications

References 68 publications

Anomalous electron-phonon coupling probed on the surface of superconductorZrB12

Anomalous electron-phonon coupling probed on the surface of superconductorZrB12

Raman evidence for nonadiabatic effects in optical phonon self-energies of transition metals

Nonadiabatic breakdown and pairing in high-Tc compounds

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