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Superconductivity

   Iron pnictides – finally a new family of high-T_c superconductors – represent a real challenge in the recent condensed matter physics. Despite an enormous effort during less than 1 year after their appearance many puzzles remain unsolved. One of the important questions concerns the superconducting order parameter in these systems with a strongly multiband character.
   Similarly to the high-T_c cuprates the superconductivity in iron pnictides is enabled by chemical doping of the antiferromagnetic parental compounds which in contrast to the cuprates are metallic. The highest transition temperature (up to 56 K) among different iron pnictides has been achieved in the optimally doped REFe-AsO(F), or the 1111 group with Gd, Nd, or Sm standing for a rare element RE. Considerable interest has also been attracted by another class of iron pnictide superconductors based on AFe₂As₂ with A = Ba, Sr and Ca, referred to as the 122-type group. The 122-type compounds are chemically and structurally simpler and less anisotropic than the 1111 ones. The maximum T_c of 38 K is obtained in the optimally hole doped Ba_0.6K_0.4Fe₂As₂ system but also the electron doped Ba(Fe_1-xCo_x)₂As₂ crystals with T_c about 25 K are available. In contrast to the 1111 systems the 122-type parent compounds show magnetic (from paramagnetic to SDW antiferromagnetic phase) and structural transition (from tetragonal to orthorhombic phase) at the same temperature of about 140 K. This transition is gradually suppressed by chemical doping but the phase diagram temperature versus doping shows an overlap between the SDW/orthorhombic and superconducting phases for x = 0.2–0.4 in Ba_1-xK_xFe₂As₂. The multiband/multigap superconductivity with interband interactions leading to an exotic s-wave pairing with a sign reversal of the order parameter between different FS sheets stands among the hot candidates to explain the high-T_c superconductivity in iron pnictides.

   Now, most of the measurements including oure point contact Andreev reflection measurements agree on existence of multiple nodeless gaps in the excitation spectrum of this multiband system. The gaps have basically two sizes – the small one with a strength up to the BCS weak coupling limit and the large one with a very strong coupling with 2D_L/kTc > 6–8. In the electron doped Ba(Fe_1-xCo_x)₂As₂ the most of the experiments including our point contact measurements reveal in quite broadened spectra only a single gap with a strong coupling strength [1]. The high precision ARPES measurements on this system identified two gaps but very close to each other, both showing a strong coupling with 2D/kT_c ~ 5 and 6, respectively.

   Fig.1 shows temperature evolution of one spectrum [2]. All the spectra at different temperatures (lines) were normalized to the conductance measured at 27 K and fitted to the BTK model with a proper temperature smearing involved. Obviously, the spectrum at the lowest temperature reminds the two gap spectrum of MgB₂ for a highly transparent junction with conductance enhancements due to Andreev reflection of quasiparticles. As the temperature is increased the double enhanced point contact conductance corresponding to two energy gaps is gradually smeared out and spectrum intensity decreases. Indeed, the spectra could be well fitted to the two gap BTK formula. The best fit for each temperature is shown by open circles. The extracted values of the gaps at different temperatures are shown in right inset of the figure (symbols) following nicely a BCS prediction (lines) rescaled to the size of the respective gap. The values of the energy gaps at lowest temperature are for the small D_S ~ 2.7 meV and the large one D_L ~ 9.2 meV, which correspond to the coupling strengths 2D_SkT_c ~ 2.7 and 2D_L/kT_c ~ 9 for T_c = 23 K. The smearing parameters (about 60% of the respective gap values), the barrier strengths z ~ 0.3 and 0.6 as well as the weight factor a ~ 0.5 obtained at 4.4 K were kept constant at higher temperatures. From the data obtained on more junctions we observe that the gaps are scattered as 2D_S/kT_c ~ 2.5–4 and 2D_L/kT_c ~ 9–10.

Figure 1: Normalized PCAR spectra of the Ba_0.55K_0.45Fe₂As₂ single crystal in the ab plane showing two superconducting gaps. Lower curves are vertically shifted for clarity. Circles represent the best fits to the two gap BTK formula. Left inset—raw data taken at 4.4 and 27 K, right inset—temperature dependence of two gaps, solid lines show BCS-type behavior of energy gaps.

   Similarly we have performed systematic studies of the NdFeAsOF superconducting energy gap using point-contact Andreev-reflection (PCAR) spectroscopy [3]. At low temperatures the PCAR conductance spectra show a pair of gap-like peaks at about ±(4–7) mV and in most cases also a pair of humps at around ±10 mV. Fits to the s-wave two-gap model of the PCAR conductance allowed to determine two superconducting energy gaps in the system. The values of the gaps are D₁ = 5 ± 1 meV and D₂ = 11 ± 2 meV, indicating very weak coupling in the band with the small gap with 2D₁/k_BT_c = 2.6 ± 0.1 and strong coupling for the second band with 2D₂/k_BT_c = 5.7 ± 0.5. Also, an indication for a reduced DOS in the normal state or pseudogap persisting well above the bulk transition temperature is found in the system.

Using specific heat (Cp) and Hall-probe magnetization experiments we investigated the extent of the vortex-liquid state in underdoped single crystals of the oxypnictide superconductors NdFeAs(O,F) and (Ba,K)Fe₂As₂ [4]. In both materials, the vortex liquid lies entirely in the regime where the three-dimensional lowest Landau-level (3D-LLL) approximation is valid and both systems present a very small shift in the specific heat anomaly with increasing field. The irreversibility line, defined as the onset of diamagnetic response, is very rapidly shifted toward lower temperatures in NdFeAs(O,F) but remains close to the Cp anomaly in (Ba,K)Fe₂As₂. These measurements strongly suggest that a vortex-liquid phase occupies a large portion of the mixed-state phase diagram of NdFeAs(O,F) but not in (Ba,K)Fe₂As₂. This difference can be attributed to different Ginzburg numbers Gi, the latter being about 100 times larger in NdFeAs(O,F) than in (Ba,K)Fe₂As₂. The angular dependence of the upper critical field, derived from 3D-LLL scaling of the irreversibility lines, presents deviations from the standard 3D effective-mass model in both materials with an anisotropy being about three times smaller in (Ba,K)Fe₂As₂ (~2.5) than in Nd(F,O)FeAs (~7.5).


Figure 2: (a) Temperature dependence of the ac transmittivity and specific heat for the indicated field values (H_a||c) in a NdFeAs(O,F) crystallite emphasizing the large difference between the position of the irreversibility line (onset of diamagnetic response at 213 Hz: vertical lines) and the specific-heat jump. (b) Similar data for (Ba,K)Fe₂As₂, showing that the specific heat and the susceptibility data both present only a minor downward shift with applied field. The paramagnetic bump observed in both systems [although larger in (Ba,K)Fe₂As₂ than in NdFeAs(O,F)] reflects the presence of T_c inhomogeneities in the platelets. However the reduced shift is observed on all probe positions, open symbols corresponding to the center of the sample, and closed symbols to the sample edge (with a slightly higher T_c value). Inset: temperature dependence of the specific heat of a (Ba,K)Fe₂As₂ crystal for H_a||c = 3 T (closed symbols) and H_a||ab=7 T (open symbols).

[1] P. Samuely, Z. Pribulová, P. Szabó, G. Pristáš, S.L. Bud’ko, P.C. Canfield, Physica C 469 (2009) 507–511.
[2] P. Szabó, Z. Pribulová, G. Pristáš, S. L. Bud’ko, P. C. Canfield, and P. Samuely, Phys. Rev. B 79, 012503 (2009).
[3] P Samuely, P Szabó, Z Pribulová, M E Tillman, S L Bud’ko and P C Canfield, Supercond. Sci. Technol. 22 (2009) 014003.
[4] J. Kačmarčík, C. Marcenat, T. Klein, Z. Pribulová, C. J. van der Beek, M. Konczykowski, S. L. Budko, M. Tillman, N. Ni, and P. C. Canfield, Phys. Rev. B 80, 014515 (2009).

P. Szabó, P. Samuely, Z. Pribulová, J. Kačmarčík, G. Pristáš(Inst. Exp.Physics, Košice, Slovakia)
C. Marcenat, (CEA-DRFMC, Grenoble, FR),
T. Klein (LEPES CNRS, Grenoble, FR)
P.C. Canfield, S.L. Buďko, M.E. Tillman (Ames laboratory, USA)