Doping and critical-temperature dependence of the energy gaps in Ba(Fe${}_{1\ensuremath{-}x}$Co${}_{x}$)${}_{2}$As${}_{2}$ thin films

Doping and critical-temperature dependence of the energy gaps in Ba(Fe $_{1 - x}$ Co $_{x}$ ) $_{2}$ As $_{2}$ thin films

P. Pecchio, D. Daghero, G. A. Ummarino, R. S. Gonnelli, F. Kurth, B. Holzapfel, and K. Iida

Phys. Rev. B 88, 174506 – Published 11 November 2013

Abstract

The dependence of the superconducting gaps in epitaxial Ba(Fe $_{1 - x}$ Co $_{x}$ ) $_{2}$ As $_{2}$ thin films on the nominal doping $x$ ( $0.04 ⩽ x ⩽ 0.15$ ) was studied by means of point-contact Andreev-reflection spectroscopy. The normalized conductance curves were well fitted by using the two-dimensional Blonder-Tinkham-Klapwijk model with two nodeless, isotropic gaps—although the possible presence of gap anisotropies cannot be completely excluded. The amplitudes of the two gaps $Δ_{S}$ and $Δ_{L}$ show similar monotonic trends as a function of the local critical temperature $T_{c}^{A}$ (measured in the same point contacts) from 25 K down to 8 K. The dependence of the gaps on $x$ is well correlated to the trend of the critical temperature, i.e., to the shape of the superconducting region in the phase diagram. When analyzed within a simple three-band Eliashberg model, this trend turns out to be compatible with a mechanism of superconducting coupling mediated by spin fluctuations, whose characteristic energy scales with $T_{c}$ according to the empirical law $Ω_{0} = 4.65 k_{B} T_{c}$ , and with a total electron-boson coupling strength $λ_{tot} = 2.22$ for $x ⩽ 0.10$ (i.e., up to optimal doping) that slightly decreases to $λ_{tot} = 1.82$ in the overdoped samples ( $x = 0.15$ ).

Received 1 August 2013

DOI:https://doi.org/10.1103/PhysRevB.88.174506

Authors & Affiliations

P. Pecchio, D. Daghero, G. A. Ummarino, and R. S. Gonnelli

Dipartimento di Scienza Applicata e Tecnologia, Politecnico di Torino, 10129 Torino, Italy

F. Kurth, B. Holzapfel, and K. Iida

Leibniz-Institut für Festkörper-und Werkstoffforschung (IFW) Dresden, P.O. Box 270116, 01171 Dresden, Germany

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Vol. 88, Iss. 17 — 1 November 2013

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Figure 1
Temperature dependence of the spectrum of a point contact on an 8% Co-doped film, up to the critical temperature and above. The shift of the spectra is clearly seen. The left inset shows the low-temperature spectrum and the polynomial curve that fits its tails used for normalization. The right inset reports the temperature dependence of the resistance of the film. The shift of the spectra correlates with the onset of resistivity in the film. Here, $T_{c}^{A}$ is between 25.20 and 25.67 K, i.e., $T_{c}^{A} ≃ 25.4 \pm 0.3$ .Reuse & Permissions
Figure 2
Low-temperature normalized PCARS spectra (symbols) in films with different Co content: $x = 0.04$ (a), $x = 0.08$ (b), $x = 0.10$ (c), and $x = 0.15$ (d), together with their two-band 2D-BTK fit (lines). The corresponding fitting parameters are listed in Table . The gap values $Δ_{S}$ and $Δ_{L}$ indicated in the panels are instead the average over different possible fits of the same curve, as explained in the text. The normal-state resistance of the contacts is also indicated, as well as the local critical temperature $T_{c}^{A}$ .Reuse & Permissions
Figure 3
(a), (b) Two examples of PCARS spectra taken in different films of $Ba {({Fe}_{0.92} {Co}_{0.08})}_{2} {As}_{2}$ . Despite the different shape of the spectra, the gap values obtained from the fit are consistent. The fit shown in (a) was obtained with $Δ_{S} = 4.25$ meV, $Γ_{S} = 3.60$ meV, $Z_{S} = 0.25$ , $Δ_{L} = 9.90$ meV, $Γ_{L} = 4.70$ meV, $Z_{L} = 0.34$ , $w_{L} = 0.60$ . The fit in (b) was obtained with $Δ_{S} = 3.70$ meV, $Γ_{S} = 2.35$ meV, $Z_{S} = 0.18$ , $Δ_{L} = 9.00$ meV, $Γ_{L} = 3.25$ meV, $Z_{L} = 0.30$ , $w_{L} = 0.40$ . (c) Gap amplitudes as a function of the resistance of the contacts, which shows the absence of any correlation between these quantities and demonstrates the spectroscopic nature of the contacts. This panel includes data taken in three different films.Reuse & Permissions
Figure 4
(a), (b) Two examples of PCARS spectra taken in different points of the same film ( $5 \times 5 {mm}^{2}$ ) of $Ba {({Fe}_{0.96} {Co}_{0.04})}_{2} {As}_{2}$ . The spectrum in (a) shows clear shoulders around 7 meV and conductance maxima at lower energy. The solid line represents the best fit of the curve obtained within the 2D-BTK model assuming that the shoulders are due to a superconducting gap $Δ^{*}$ . The fitting parameters are $Δ_{L} = 2.8$ meV, $Γ_{L} = 1.15$ meV, $Z_{L} = 0.24$ , $Δ^{*} = 9.8$ meV, $Γ^{*} = 4.75$ meV, $Z^{*} = 0.25$ , $w_{S} = 0.2$ . The spectrum in (b) instead does not show shoulders but a single maximum at zero bias, and the FWHM of the whole structure is of the order of 3 meV. The solid line is the two-band BTK fit, obtained with parameters $Δ_{S} = 1.35$ meV, $Γ_{S} = 0.84$ meV, $Z_{S} = 0.18$ , $Δ_{L} = 2.6$ meV, $Γ_{L} = 1.8$ meV, $Z_{L} = 0.4$ , $w_{S} = 0.6$ . The dashed line is the single-band BTK fit, obtained with parameters $Δ = 1.92$ meV, $Γ = 1.74$ meV, $Z = 0.12$ . A magnification of the low-energy region (inset) shows that the two-gap fit is better. (c) Amplitudes of the “gap” $Δ^{*}$ and of the gaps $Δ_{S}$ and $Δ_{L}$ as a function of the contact resistance $R_{N}$ .Reuse & Permissions
Figure 5
Average gap amplitudes in Ba(Fe $_{1 - x}$ Co $_{x}$ ) $_{2}$ As $_{2}$ thin films with different Co content obtained by PCARS measurements (filled circles), plotted as a function of $T_{c}^{A}$ . The other data points are taken from literature, and specifically squares from Ref. 40, up triangles from Ref. 24, diamonds from Ref. 47, down triangles from Ref. 12, left triangles from Ref. 9, stars from Ref. 65, asterisks from Ref. 13, right triangles from Ref. 49, hexagons from Ref. 48, half-filled squares from Ref. 46, half-filled circles from Ref. 10, and half-filled triangles from Ref. 50. The techniques used for these measurements are indicated in the legend. The upper and lower dashed lines correspond to a gap ratio $2 Δ / k_{B} T_{c}$ equal to 3.52 and 9.0, respectively.Reuse & Permissions
Figure 6
Doping dependence of the gaps measured by PCARS (circles, left vertical scale) and of the critical temperature from resistivity measurements (lines, right vertical scale). Triangles and squares indicate the values of the gaps and of the critical temperature calculated within the three-band Eliashberg model described in the text. The inset shows the dependence of the coupling strengths $λ_{12}$ and $λ_{13}$ on the Co content, together with the total electron-boson coupling constant.Reuse & Permissions

Physical Review B

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Doping and critical-temperature dependence of the energy gaps in Ba(Fe $_{1 - x}$ Co $_{x}$ ) $_{2}$ As $_{2}$ thin films

P. Pecchio, D. Daghero, G. A. Ummarino, R. S. Gonnelli, F. Kurth, B. Holzapfel, and K. Iida

Phys. Rev. B 88, 174506 – Published 11 November 2013

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Physical Review B

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Doping and critical-temperature dependence of the energy gaps in Ba(Fe1−xCox)2As2 thin films

P. Pecchio, D. Daghero, G. A. Ummarino, R. S. Gonnelli, F. Kurth, B. Holzapfel, and K. Iida

Phys. Rev. B 88, 174506 – Published 11 November 2013

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Doping and critical-temperature dependence of the energy gaps in Ba(Fe $_{1 - x}$ Co $_{x}$ ) $_{2}$ As $_{2}$ thin films