Electron Tunneling Spectroscopic Measurements on Al-doped MgB2 Thin Films

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Physics Procedia 36 (2012) 479 – 484

Superconductivity Centennial Conference

Electron tunneling spectroscopic measurements on Al-doped MgB2 thin films A.G. Zaitseva*, R. Schneidera, O. de la Peña-Seamana,b, R. de Cossb, R. Heida, K.-P. Bohnena and J. Geerka a

b

Karlsruher Institut für Technologie, Institut für Festkörperphysik, D-76021 Karlsruhe, Germany Departamento de Fisica Aplicada, Centro de Investigación y de Estudios Avanzados del IPN, 97310 Mérida, Yucatán, Mexico

Abstract The effect of Al-doping on the electron-phonon coupling in magnesium diboride films was studied by electron tunneling spectroscopy on planar sandwich-type Mg1-xAlxB2-oxide-indium junctions. The superconducting Mg1-xAlxB2 films (0 ” x < 0.5) were prepared in situ by simultaneous sublimation of Mg and sputtering of B and Al. The oxide barrier was either natural or artificial (aluminium oxide). The high junction quality allowed precise measurements of the differential conduction up to high bias-voltages of 120 mV. In the low bias range the small energy gap Δπ was measured: it decreased linearly with increasing Al-doping in agreement with the band filling model. The measurements at higher energies revealed the phonon induced features in the electron density of states. Although the spectra were influenced by the proximity effect below ∼20meV, they enabled the determination of the effective Eliashberg function α2F. For the same film compositions α2F data were obtained theoretically from first principles calculations. The progressive loss of superconductivity with increasing Al doping was reflected in both the experiment and calculations by the evolution of α2F. The dominating π-σ interband pairing interaction, which contributes most to the superconductivity on the π sheet, was gradually weakened in correlation with the band structure calculations.

© Rogalla and © 2011 2012 Published Published by by Elsevier Elsevier Ltd. B.V.Selection Selectionand/or and/orpeer-review peer-reviewunder underresponsibility responsibilityof ofHorst the Guest Editors. Peter Kes. Keywords: magnesium diboride; superconducting thin films; tunneling spectroscopy; electron-phonon coupling

The tunneling spectroscopy on superconducting planar sandwich-type junctions was developed by McMillan and Rowell [1] in the 1960s. Further improvement of this technique during the later decades approved it to be one of the most reliable and precise methods for the straight-forward experimental study

* Corresponding author. E-mail address: [email protected]

1875-3892 © 2012 Published by Elsevier B.V. Selection and/or peer-review under responsibility of the Guest Editors. doi:10.1016/j.phpro.2012.06.221

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of the electron-phonon coupling mediated superconductivity including the electron reduced density of states (RDOS) and the Eliashberg function [2]. The latter, α2( ω)F( ω), is a function of the phonon energy ƫ ω. It is comprised by F( ω), which is the phonon density of states, and α2( ω), which is the related electron-phonon coupling strength averaged over directions in k space. The key limitation of this powerful technique is the preparation of the tunnel junctions themselves, which remains an issue of thorough optimisation finally dependent on the fundamental chemistry of the examined superconductor. With respect to magnesium diboride, a successful preparation of the tunnel junctions on the basis of pure MgB2 thin films has been reported in our earlier work [3]. The resulted measurements gave an additional experimental prove, that MgB2 is indeed a phonon-mediated superconductor and, moreover, that its dominating feature is the interband pairing interaction described by α2Fπ-σ. Further efforts led to the preparation of the high-quality junctions on the basis of the Al-doped MgB2 thin films, which were potentially promising for the tunneling spectroscopy, as reported two years ago at the last EUCAS conference [4]. In our present contribution we report the application of the tunneling spectroscopy for investigating the effect of aluminum doping on the electron-phonon coupling in the magnesium diboride thin films. The obtained experimental results are directly compared with theoretical calculations using the band filling model and first principles band structure calculations of RDOS and Eliashberg function. This study was made possible due to the recent progress in the preparation of high quality superconducting Mg1-xAlxB2 thin films and sandwich-type cross-striped tunnel junctions [4,5]. The Mg1-xAlxB2 films were prepared in situ by simultaneous sublimation of Mg and sputtering of B and Al. The film composition and especially the Al content (x) were determined by Rutherford Backscattering Spectrometry with the accuracy of Δx ≈ 0.02. For the present work the films of 300 nm thickness were prepared on rplane and c-plane sapphire substrates of 10×20 mm2 size. The films were textured, with c-axis normal to the film surface. The superconducting transition temperature, Tc, of these films varied almost linearly with their Al content from 35 K (x = 0) to 4K (x → 0.5), see Fig. 1, left inset. The Mg1-xAlxB2 film served as a base electrode for the required junction. On the film surface the insulating oxide barrier was formed and the indium counter-electrode was evaporated onto this barrier. This barrier was either natural or artificial (aluminium oxide). The obtained junctions were stable with respect to electrical breakdown up to high bias voltages of at least 600 mV and enabled reproducible low-noise measurements of currentvoltage characteristics and their first and second derivatives, dI/dV and d2I/dV2, respectively. A series of dI/dV measurements was performed in the low-bias range of ±10 mV at 1.2 K and zero applied magnetic field, where both Mg1-xAlxB2 and indium are superconducting (superconductor-insulator-superconductor, or SIS, junction), in order to determine the energy gap of the Mg1-xAlxB2 films with different Al content [4]. The measurements standardly revealed a typical BCS-like energy gap with low leakage current of ≤ 1% of the conductance peaks, which was clearly the superposition of the small energy gap Δπ of Mg1-xAlxB2 and the gap of superconducting indium ΔIn = 0.54 meV. A characteristic example of such gap is shown in the right inset of Fig 1. None of around 70 junctions examined for this work revealed the large σ gap. The value of the small energy gap decreased almost linearly with the Tc of the samples, see Fig. 1, which is in agreement with predictions of the band-filling model [5,6]. The technical details of the tunnel measurements on the Mg1-xAlxB2/oxide/In junctions in the phonon energy range (20 ÷ 120 mV) were reported previously [4]. The strategy of the further analysis of the tunneling spectroscopy data is the following [1-3]. The quantity to be measured via a tunnel junction between the superconductor and the normal metal is the quasiparticle density of states. It contains phonon-induced features observed in the differential conductance well above the energy gap region. These features are used to compute α2F via the Eliashberg equation. In the example shown in Fig. 2(a) for an Mg0.89Al0.11B2based junction the phonon-induced features make the difference between the conductance measured in superconducting state at 4.2 K, (dI/dV)S, and the curve measured in normal state at 30 K, (dI/dV)N. A direct way to observe the phonon features experimentally is to measure the derivative of the differential conductance [4]. The features are seen as peaks in -d2I/dV2 after the normal conducting background is subtracted,

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TC (K)

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30 20 10 0

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x in Mg 1-xAlx (%) dI/dV (arb. units)

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Tc (K)

Fig. 1 Relation between the transition temperature and the π energy gap of the Mg1-xAlxB2 thin films obtained from the measurements on the SIS junctions at 1.2 K (squares) and predicted by the band filling model: dashed line [5] and solid line [6]. The right inset shows a typical gap measurement with an SIS Mg0.6Al0.4B2-based junction at 1.2 K. The left inset shows the relation between the Al content (x) of the films and their Tc.

see Fig. 2(b). Thus, the tunnelling density of states can be obtained as Nt = (dI/dV)S/(dI/dV)N, which is a function of the quasiparticle energy eV. Being measured as a function of energy starting from the gap edge E = eV - Δ it can be related to the BSC density of states NBSC(E) = E/(E − Δ)1/2 in terms of RDOS: Nred(E) = Nt(E)/NBSC(E) − 1 .

(1)

For the given example of Mg0.89Al0.11B2 RDOS obtained from the data of Fig. 2 (a) according to (1) is shown in Fig. 2 (c) as experimental data. It should be emphasized, that generally the integral of RDOS is zero, i.e. its area below the energy axis must be exactly equal to the area above the axis. This ‘sum rule’ results from the conservation of particle number, when going from the normal to superconducting state. As an example, the RDOS obtained for pure MgB2 films can be considered [3]. However, RDOS obtained for our Mg1-xAlxB2 films were typically depressed below zero level, particularly strong at low energies in the gap region below ∼20 meV, see Fig. 2 (c). The most likely explanation is the proximity effect due to a minor presence of metallic Al in the tunnel barrier, which makes a part of the energy states below the gap occupied. Consequently, the further inversion of the obtained RDOS data into the Eliashberg function was performed using the McMillan-Rowell computer code corrected for the proximity effect, PMMR [5]. Compared to the similar code for proximity-free junctions, e.g. used in the case of pure MgB2 [3], the PMMR code contains two fit parameters d/l and R. Here d is the thickness of the normal conducting proximity layer between the insulating tunnel barrier and the superconducting film, l is the effective scattering length and R = 2d/hvF, with vF as Fermi velocity for the normal conductor. In practice both parameters are varied until the RDOS returned by the computer code reproduces the experimental one reasonably well. Our best fit shown in Fig. 2(c) was obtained for the values d/l = 0.4 and R = 0.002 meV-1. Assuming vF = 1.4×106 m/s for aluminium one obtains d ≈ 9Å and l ≈ 2.2 nm, which seem to be reasonable values. The Eliashberg function generated by the PMMR code is shown in Fig. 2 (d). As anticipated, the peaks in α2F reproduce qualitatively the peaks of −d2I/dV2, compare Fig. 2 (b) and (d).

A.G. Zaitsev et al. / Physics Procedia 36 (2012) 479 – 484

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-4

dI / dV (10 S)

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Fig. 2. Differential conductance (a) measured at 4.2 K with superconducting Mg0.89Al0.11B2 (solid line) and at 30 K with normal conducting Mg0.89Al0.11B2 (broken line). Its negative second derivative (b) with subtracted normal-state background. Reduced density of states (c) determined from the dI/dV data (solid line) and calculated using the PMMR-program (circles). The resulting Eliashberg function (d).

The obtained α2F data were compared with the results of theoretical calculations. For this purpose the Mg1-xAlxB2 was modelled ab-initio in the self-consistent virtual-crystal approximation implemented within the mixed-basis pseudopotential method, see [5] for details. Finally the individual Eliashberg functions for both π and σ sheets and their combination were computed for a series of Mg1-xAlxB2 compositions in the range 0 ≤ x < 0.4 corresponding to our experiment. Characteristic examples are shown in Fig. 3. Then, the related RDOS of the π sheet were calculated using the individual Eliashberg functions shown in Fig. 3. These theoretical RDOS were processed in the same way as the experimental ones, namely inverted into the effective Eliashberg functions using the standard MMR computer code. The results are shown in Fig. 4 and compared with the correspondent experimental data. For pure MgB2 (x = 0) the spectra are basically comprised by three broad peaks. Actually, the central peak around 60 meV is resolved in two parts in the calculated α2F, see Fig. 2 (b). It should be noted, that such fine structures of this middle peak were indeed observed in the tunneling measurements on the junctions of the highest quality [7]. It has

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3 X=0

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π−π π−σ σ−σ

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Energy (meV)

Fig. 3. Individual Eliashberg functions (α2F)π-π, (α2F)π-σ and (α2F)σ-σ calculated ab-initio for the Mg1-xAlxB2/oxide/In junctions with different Al contents (a) x = 0; (b) x = 0.11; (c) x = 0.29; (d) x = 0.39.

been shown earlier in detail [3], that this central peak resulting from the π-σ interband pairing interaction is mainly responsible for the superconductivity of the π sheet. With increasing Al doping the Eliashberg function evolves as following. The overall three-peak configuration is roughly preserved. The low energy peak at around 40 meV, which is due to acoustic phonons [3], remains fairly unaffected by the substitution of Mg by Al. Apparently, it does not contribute much to the electron-phonon coupling responsible for the superconductivity in Mg1-xAlxB2. Both theory and experiment reveal, that the increasing Al doping affects the shape and reduces the spectral weight of the central peak, which is supposed to be primarily responsible for the electron-phonon coupling. This correlates with the gradual loss of superconductivity observed in the Al doped films, which results in decreasing Tc as well as Δπ, see Fig. 1 and the insets in Fig. 4. Increasing the Al content x from 0 to 0.39 also affects the peak of high-energy optical phonons at above 90 meV. In both experimental and theoretical spectra this peak increases dramatically and spreads to higher energies. These observations are in agreement with the renormalisation of the phonon density of states observed in bulk samples by inelastic neutron scattering [8].

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x=0

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Tc = 33 K Δπ = 2.6 meV

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Fig. 4. Eliashberg functions obtained by the inversion of the experimental data (a) to (d) and theoretical data (e) to (h) of Mg1-xAlxB2 with different Al content x. The Tc and Δπ values of each composition are given in the insets.

In summary, the effect of Al doping on the electron-phonon coupling in magnesium diboride thin films was studied experimentally by means of tunneling spectroscopy on Mg1-xAlxB2-oxide-In planar junctions. It was observed that the small energy gap Δπ decreases linearly with increasing Al-doping in agreement with the band filling model. The spectra in the phonon energy range enabled the determination of the Eliashberg function. For the same film compositions α2F data were obtained theoretically from first principles calculations. Both experiment and theory indicated, that the Al doping gradually weakens the π-σ interband pairing interaction, which contributes most to the superconductivity on the π sheet. Another effect of Al doping was the spread of the spectrum to higher energies.

References [1] McMillan WL, Rowell JM in Superconductivity, edited by R. D. Parks (Dekker, New York, 1969), Vol. 1, p. 561. [2] Geerk J, v.Löhneysen H. Phys. Rev. Lett. 2007, 99, 257005. [3] Geerk J, Schneider R, Linker G, Zaitsev AG, Heid R, Bohnen K-P, v.Löhneysen H. Phys Rev Lett 2005; 94: 227005. [4] Zaitsev AG, Schneider R, Geerk J. J Phys Conf Ser 2010; 234: 042039. [5] Schneider R, Zaitsev AG, de la Peña-Seaman O, de Coss R, Heid R, Bohnen K-P, Geerk J. Phys Rev B 2010; 81: 054519. [6] Kortus J, Dolgov OV, Kremer RK, Golubov AA. Phys Rev Lett 2005; 94: 027002. [7] Schneider R, Geerk J, Zaitsev AG. Appl. Phys. Lett. 2007; 91: 022509. [8] Renker B, Bohnen K-P, Heid R, Ernst D, Schober H, Koza M, Adelmann P, Schweiss P, Wolf T. Phys Rev Lett 2002; 88: 067001.