Anomalous electron-phonon coupling probed on the surface of superconductorZrB12

Abstract

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...

Effect of Pressure on the Ginzburg-Landau Parameterκ=λ/ξinYB6

“…Note that the independence of the ratio 2∆(0)/k B T c of pressure was recently confirmed for RbOs 2 O 6 [13] and ZrB 12 [14] BCS superconductors. The resulting λ(0) vs. p dependence is shown in the inset of the Fig.…”

Theoretical elastic stiffness and thermodynamic properties of zirconium dodecaboride from first principles calculation

“…In the late 1960s, Matthias et al [2] found that ZrB 12 has the highest superconducting critical temperature (T c % 6 K) in several of metal dodecaborides (M = Sc, Y, Zr, La, Lu, and Th). In order to understand its superconducting behavior, this compound has been widely studied in virtue of recent progress in growing large high quality single crystals of dodecaborides [3][4][5][6][7][8]. It was previously considered that the superconductivity in ZrB 12 is directly connected with the vibrations of boron complexes [3].…”

Effect of electron-phonon coupling on the superconducting transition temperature in dodecaboride superconductors: A comparison ofLuB12withZrB12Teyssier1, Lortz2, Petrović3 et al. 2008Phys. Rev. BSelf Cite464410View full textAdd to dashboardCite

“…33 For ZrB 12 , an electron-phonon coupling constant Х 1 was extracted in this way, in agreement with previous reports. [34][35][36] Figure 8 shows a comparison at low temperature of the low-frequency part of the reflectivity for the two compounds. The fits, including the contribution from the electron-phonon interaction as described above, are presented by a solid red line.…”