Orbital-Independent Superconducting Gaps in Iron Pnictides

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Science  29 Apr 2011:
Vol. 332, Issue 6029, pp. 564-567
DOI: 10.1126/science.1202150


The origin of superconductivity in the iron pnictides has been attributed to antiferromagnetic spin ordering that occurs in close combination with a structural transition, but there are also proposals that link superconductivity to orbital ordering. We used bulk-sensitive laser angle–resolved photoemission spectroscopy on BaFe2(As0.65P0.35)2 and Ba0.6K0.4Fe2As2 to elucidate the role of orbital degrees of freedom on the electron-pairing mechanism. In strong contrast to previous studies, an orbital-independent superconducting gap magnitude was found for the hole Fermi surfaces. Our result is not expected from the superconductivity associated with spin fluctuations and nesting, but it could be better explained invoking magnetism-induced interorbital pairing, orbital fluctuations, or a combination of orbital and spin fluctuations. Regardless of the interpretation, our results impose severe constraints on theories of iron pnictides.

The high-transition-temperature (Tc) superconducting iron pnictides (1) of the BaFe2As2 (Ba122) family exhibit a typical phase diagram (Fig. 1A) in which the parent compound remains metallic through an antiferromagnetic (AF) spin-ordering transition at TN and a tetragonal-to-orthorhombic structural transition at TS (2, 3). Both TN and TS decrease in a similar fashion upon ion substitution and lead to an emergent dome-shaped superconducting (SC) phase with a high Tc of up to 55 K (4). Such high Tcs are not expected from a conventional electron pairing through lattice vibrations (5). Focusing on the nesting tendency connecting quasi-cylindrical Fermi surfaces (FSs), electron pairing mediated by the AF spin fluctuations has been argued (6, 7).

Fig. 1

(A) Schematic phase diagram of BaFe2(As,P)2 and (Ba,K)Fe2As2. TN represents the AF transition temperature and TS a tetragonal to orthorhombic structural transition temperature. Red arrows indicate stripe-type AF spin ordering on the orthorhombic lattice. Inset shows calculated FSs of optimally doped BaFe2(As,P)2. (B) Momentum cut along kz axis corresponding to the gray rectangle in the inset of (A). FS profile of BaFe2(As,P)2 reported in (22) is indicated by the gray curve. (C and D) Hole band dispersions around the zone center measured by synchrotron radiation photon sources of hν = 10 eV and 7 eV, respectively. Inner (kF1) and outer (kF2) Fermi momenta are estimated by plotting the peak positions of MDCs below EF. Comparing the kF dispersions along the kz axis (22), momentum cuts measured by hν = 7 eV and 10 eV are superimposed as black curves at the bottom of (B). (E) Quantitative comparison of the kF measured by hν = 7 eV and 63 eV, indicating reliable determination of kz = π. Black circles represent kF1 (nearly degenerate inner and middle hole bands in Fig. 2B) and kF2 (outer hole band in Fig. 2C) obtained by synchrotron radiation photon source of hν = 7 eV. The gray curve represents FSs obtained by hν = 63 eV (22).

On the other hand, there is a proposal that orbital ordering (810), which causes inequivalency of the Fe 3d partial density of states, occurs at TS. This phenomenon could give rise to C2 symmetric physical properties that cannot be expected from only 1% lattice distortion at TS. In particular, inequivalent occupation of the xz and yz orbitals (x, y, and z represent orthorhombic axes) near the Fermi level (EF), as observed by angle-resolved photoemission spectroscopy (ARPES), indicates the potential role of orbital degrees of freedom (11). Based on the multiorbital nature of iron pnictides, SC pairing through orbital fluctuations has been proposed (1215).

Experimental evidence has favored different SC pairing symmetries. Sign-reversal superconductivity suggested by scanning tunneling microscopy on Fe(Te,Se) (16) and inelastic neutron spectroscopy on (Ba,K)Fe2As2 (17) is consistent with the s± wave symmetry expected from spin fluctuations. The robustness of Tc against the impurities in LaFeAs(O,F) (18) suggests the s++ wave superconductivity, which may be caused by orbital fluctuations. Such material dependence in pairing symmetry can also arise from the balance of these two pairing mechanisms because a crossover from s± to s++ symmetry may occur, depending on the strengths of microscopic electronic parameters (1215). However, to date there has been no experimental evidence for the role of orbital fluctuations on the superconductivity in the pnictides.

The pairing mechanism will be reflected in the momentum dependence of the SC gap properties. Spin fluctuation mechanism predicts strongly orbital-dependent SC gap magnitude (7, 19), but orbital fluctuations should eliminate such orbital dependence (1315). Because each FS sheet in iron pnictides has a distinct d-orbital character, probing the FS dependence of the SC gap magnitude will be a crucial test for identifying the contribution of the orbital fluctuations in the electron pairing. Here, we report the FS dependence of the SC gap magnitude of representative iron-pnictide superconductors BaFe2(As0.65P0.35)2 (AsP122) and Ba0.6K0.4Fe2As2 (BaK122) by using bulk-sensitive laser-ARPES (20) [see section 1 of the supporting online material (SOM)].

ARPES, using a fixed photon energy (hν), probes a specific profile of the in-plane FSs perpendicular to the momentum axis along the z direction kz. Especially for AsP122 with strong FS warping, the orbital character depends on the kz value (21). Estimation of kz value corresponding to 7 eV photons of laser-ARPES is thus necessary for investigating the orbital dependence of the SC gap magnitude. Figure 1B is a schematic of the experimental FS profile along the kz axis of AsP122 taken from (22). Whereas the inner hole FS is almost cylindrical, the outer one gets enlarged toward kz = π, consistent with the band calculations (inset of Fig. 1A) (21). We used a synchrotron radiation photon source of 10 eV and 7 eV to find this characteristic warping in the inner (kF1) and outer (kF2) Fermi momenta. As shown in Fig. 1, C and D, separation between kF1 and kF2 in C was three-fourths of that in D, which indicates that 7 eV photons probe the FS profile at kz ~ π to 1.2π. This estimate of kz for hν = 7 eV was also quantitatively confirmed by the comparable FS size obtained by the higher photon energy of 63 eV probing kz ~ π (22) (Fig. 1E).

High-resolution laser-ARPES E-k images for AsP122 (Fig. 2, B and C) are along cut 1 and 2 indicated in Fig. 2A, respectively. Both the inner and middle hole bands were resolved as the two-peak feature in the momentum distribution curve (MDC) near EF (Fig. 2B), although they are nearly degenerate in Fig. 1, C and D. We could separate three hole bands along cut 1 and 2. The temperature (T) dependence of the energy distribution curves (EDCs) at kF in cut 2 (outer FS) shows the SC gap opening below bulk Tc (Fig. 2D), and the SC gap magnitude Δ was directly extracted from the fitting procedure using a Bardeen-Cooper-Schrieffer (BCS) spectral function (SOM, section 2). This Δ value is in excellent agreement with the BCS-like T dependence (inset of Fig. 2D). Figure 2, E to G, shows EDCs in the SC state and fitting results for each hole FS. A shift in the leading edge relative to EF indicates an SC gap opening. As shown in Fig. 2H, the FS angle dependence of Δ indicates the fully gapped nature of the three hole FSs in AsP122. Considering the nodal SC gap symmetry proposed by the magnetic penetration depth, thermal conductivity (23) and nuclear magnetic resonance measurements (24), our results rule out d-wave symmetry and imply the possible presence of line nodes in electron FSs around zone corners. The Δ of each hole FS is comparable to the common reduced gap value of 2Δ/kBTc ~ 3.0.

Fig. 2

Laser-ARPES on BaFe2(As0.65P0.35)2. (A) FSs around the (0,0) point of BaFe2(As0.65P0.35)2, measured by circularly polarized laser. (B and C) Band dispersions measured by circular polarization along cut 1 and cut 2 in (A), respectively. (D) T dependence of EDC at kF in cut 2. Inset shows T dependence of the SC gap magnitude determined by the fitting procedure, using the BCS spectral function. The red broken curve represents BCS-like T dependence. (E to G) Fitting results on the EDCs in the SC state measured at kF of inner, middle, and outer FS, respectively. (H) FS angle dependence of the SC gap magnitude in each hole FS. Inset shows the definition of the FS angle θ.

The laser-ARPES results on BaK122 (Fig. 3A) showed three hole FSs around the zone center, which is consistent with the first-principles band calculations with experimental lattice constants. We separately observed the three hole bands by varying the laser polarizations. Figure 3B shows the three hole bands measured by circular polarization along the momentum cut represented by the white arrow in Fig. 3A. When we chose p-polarization, the band A became dominant (Fig. 3C), in contrast to the band B and C being active in s-polarization (Fig. 3D). Such strong polarization dependence of the photoelectron intensity implies a different d-orbital character in these hole bands (11). We make use of the polarization dependence for separating band A from others to discuss its T dependence across Tc.

Fig. 3

Laser-ARPES on Ba0.6K0.4Fe2As2. (A) FSs around the (0,0) point of Ba0.6K0.4Fe2As2, measured by circularly polarized laser. (B to D) Band dispersions measured by circular, p-, and s- polarized laser, respectively. The corresponding momentum cut is shown by the white arrow in (A). (E) T dependence of EDC at kF of band A, measured by p-polarization. The contribution from other hole bands is already removed by choosing polarization, and the spectral weight at EF is very low, indicative of the clear SC gap opening. (F) EDCs divided by FD functions. They are further normalized by the divided EDC at 60 K to extract the T-dependent component. Black dots represent the peak position of peak 1, peak 1′ and peak 2. (G) T dependence of the SC gap magnitude estimated by fitting analysis using the BCS spectral function. The red broken curve represents BCS-like T dependence. (H to J) Fitting results on the EDCs in the SC state, measured in inner, middle, and outer FS, respectively. (K) FS angle dependence of the SC gap magnitude in each hole FS. Inset shows the definition of the FS angle θ.

In Fig. 3E, we show the T dependence of the EDC at kF of band A measured with a p-polarized laser. A distinct two-peak structure (peak 1 and peak 2) was observed near EF with decreasing T. To emphasize the peak 1′ in the unoccupied state, we divided EDCs using a Fermi Dirac (FD) function convoluted by a Gaussian corresponding to the experimental energy resolution. Divided spectra were further normalized by that measured at 60 K (Fig. 3F). Both peaks 1 and 1′ appeared just below bulk Tc, accompanying a gap structure centered at EF consistent with the Bogoliubov quasiparticle picture. This observation strongly suggests that peaks 1 and 1′ arise from superconductivity. However, peak 2 is found even in the normal state, which suggests that it is a non-SC peak (for its detailed analysis and possible origin, see SOM section 3).

We can quantitatively estimate ∆ for each hole FS sheet focusing on the peak 1 and gap structure around EF in a similar manner to that used for AsP122. By extracting the SC gap magnitude from a series of T-dependent EDCs in Fig. 3E, an excellent agreement with BCS-like T dependence is obtained as shown in Fig. 3G. Figure 3, H to J, shows the EDCs in the SC state and the fitting results for each hole FS in BaK122. As indicated by the leading-edge shift in EDCs at FS angles θ = 8 and θ = 45 degrees (Fig. 3H), we observed slight anisotropy in Δ. The definition of the FS angle θ and the gap anisotropy in each hole FS is summarized in Fig. 3K. In addition to the fully gapped nature, we found comparable Δ values for the three hole FSs with a small reduced gap value of 2Δ/kBTc ~ 1.7 (SOM, section 4). This result is in a strong contrast to the “two-gap” picture previously observed at around zone center (25, 26) (SOM, section 5).

The FS-sheet dependences of SC gap magnitude in AsP122 and BaK122 obtained by laser-ARPES are summarized in Fig. 4. The most remarkable feature commonly observed in AsP122 and BaK122 is the coincidence of Δ in the three hole FSs. At least for AsP122, the size and this characteristic behavior in SC gaps are observed independently of the kz values (SOM, section 6). First-principles band calculations indicate that each hole FS is characterized by a different orbital character. This property was also experimentally confirmed by the strong polarization dependence in hole bands of BaK122 (Fig. 3, B to D). The comparable Δ for all hole FSs thus indicate that they are almost orbital-independent.

Fig. 4

(A) Schematic momentum dependence of the superconducting gap magnitude around kz = π in BaFe2(As0.65P0.35)2 and Ba0.6K0.4Fe2As2, determined by laser-ARPES. Those in electron FSs around zone corners (light gray) are speculations. (B) Illustration of the electron pair scattering from (k↑,-k↓) to (k′↑,-k′↓) between disconnected FSs of the same orbital character (intraorbital pairing). Electrons are scattered by the AF spin fluctuations with the wave vector Q derived from the FS nesting. (C and D) Schematic FS profiles at kz = π for AsP122 and BaK122, respectively. The number of FS sheets and their orbital characters are based on the first-principles band calculations using experimental atomic positions of x = 0.4 (x = 0.33) for BaK122 (AsP122) with BaFe2As2 structure. FS sheets composed of ZX/YZ, X2-Y2, and 3Z2-R2 orbitals (X, Y, and Z represent tetragonal axes) are colored in blue, green, and red, respectively. Arrows with wave vector Q represent the nesting tendency between FS sheets of the same orbital character. Because 3Z2-R2 orbital electrons do not form the FSs around zone corners, they cannot participate in electron pairing through the spin fluctuations of wave vector ~ Q (15, 30).

Of course, conventional isotropic electron-phonon interaction can give a homogeneous Δ for all FSs, but this mechanism is not likely in iron pnictides for three reasons. First, high Tc up to 55 K (4) is not expected from the conventional electron-phonon interactions (5). Second, a nodal SC gap is experimentally suggested in several iron pnictides (23, 24, 27, 28). Third, material dependence of the SC gap magnitude implies electron-pair scattering between hole and electron FSs, originating in the FS nesting (SOM, section 7). We expect that the pairing mechanism is not purely of phonon mediation but is closely related to the spin fluctuations and/or orbital fluctuations. For a spin-fluctuations pairing mechanism (6, 7, 19), the SC gap is most closely related to the spin susceptibility. The calculated spin susceptibility suggests dominant electron-pair scattering between disconnected FSs composed of the same orbital character (7, 19) (intraorbital pairing), as illustrated in Fig. 4B. Then, Δ is expected to be highly sensitive to the orbital character, depending on the overlap of the FS shape it composes. This property, nevertheless, contradicts the orbital-insensitive SC gaps we observed in the laser-ARPES experiments.

In particular, we focus on the 3Z2-R2 (X, Y, and Z represent tetragonal axes) orbital because it does not contribute to the electron FSs around zone corners in 122 systems (Fig. 4, C and D) (21). In this case, intraorbital electron pairing between the disconnected FSs is suppressed, and then the Δ of the 3Z2-R2 orbital electrons should be quite small. According to the band calculations in (21), the 3Z2-R2 orbital is dominant in the outer hole FS of AsP122 around kz ~ π. This is supported by our polarization-dependent laser-ARPES, which shows a dominantly 3Z2-R2 orbital character in the outer hole FS of AsP122 (SOM, section 8). Taking this into account, the comparable size of SC gap magnitude for various orbital characters, including the 3Z2-R2 orbital, can hardly be explained by the spin-fluctuation mechanism alone.

However, the importance of interorbital coupling (29, 30) and the role of the orbital fluctuations are being theoretically raised (1215), which has been neglected in the genuine spin-fluctuations pairing mechanism. Such interorbital electron pairing is expected to dissolve the orbital dependence of Δ and can explain the comparable Δ around the zone center observed by laser-ARPES.

A multiorbital band structure near EF in iron pnictides has the potential to enhance the orbital fluctuations. In addition, orbital fluctuations are expected to evolve in the vicinity of the orbital ordered state. In the parent material of iron pnictides, antiferromagnetic ordering generally occurs accompanying the structural transition from tetragonal to orthorhombic crystal symmetry (2, 3) (Fig. 1). Recently, orbital ordering at the structural transition was theoretically proposed (810). Previous laser-ARPES on Ba122 reported unequal occupation in the electronic structure of zx and yz orbitals below the magneto-structural transition supporting the possible orbital ordering scenario (11). In addition, the spin and orbital degrees of freedom might be strongly coupled for the parent and superconducting compounds (3135). Theoretical studies have shown that superconductivity in the iron pnictides could be derived from orbital fluctuations mixed with spin fluctuations (31, 35). Considering this background, the present result is reasonably explained as an indication of the importance of orbital fluctuations for the superconductivity of the iron pnictides; this should be taken into account at least on the same footing as spin fluctuations. Thus, while a dominantly orbital-fluctuation–derived superconductivity can be somewhat speculative and needs to be confirmed by further work, our results clearly provide severe constraints for a complete theory of superconductivity in the iron pnictides.

Supporting Online Material

Materials and Methods

SOM Text

Figs. S1 to S4


References and Notes

  1. Materials and methods are available as supporting material on Science Online.
  2. Acknowledgments: We thank W. Malaeb for experimental supports and valuable discussions. We acknowledge T. Yoshida, R. Arita, H. Kontani, S. Onari, M. Ogata, and Y. Yanase for valuable discussions. We acknowledge K. Kuroki, H. Usui, Y. Suzuki, and A. Carrington for valuable discussions and first-principles band calculations. Part of this work was performed at the Hiroshima Synchrotron Radiation Center, Hiroshima university, Japan (proposal 10-B-24). Support for this work was provided by Special Coordination Funds for Promoting Science and Technology, Promotion of Environmental Improvement for Independence of Young Researchers (to K.O.). This research is supported by the Japan Society for the Promotion of Science (JSPS) through its Funding Program for World-Leading Innovative R&D on Science and Technology (FIRST) Program.
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