Anisotropy of the superconducting gap in the iron-based superconductor BaFe2(As(1-x)P(x))2.

We report peculiar momentum-dependent anisotropy in the superconducting gap observed by angle-resolved photoemission spectroscopy in BaFe2(As(1-x)P(x))2 (x = 0.30, Tc = 30 K). Strongly anisotropic gap has been found only in the electron Fermi surface while the gap on the entire hole Fermi surfaces are nearly isotropic. These results are inconsistent with horizontal nodes but are consistent with modified s ± gap with nodal loops. We have shown that the complicated gap modulation can be theoretically reproduced by considering both spin and orbital fluctuations.

In the iron-based superconductors, most of the experimental studies have so far indicated that the superconducting (SC) gap is nodeless and opens on all Fermi surfaces (FSs) in contrast to the d-wave SC gap of the high-Tc cuprate superconductors1. However, it is unclear whether the SC order parameter is a conventional s wave without sign change (s++ wave) or its sign changes between FSs (s± wave). According to theories of spin-fluctuation-mediated superconductivity, various SC gap structures, such as nodeless s±-wave, nodal s-wave, and nodal d-wave, are realized depending on the FS geometry234. On the other hand, observation of orbital-polarized states5 and the strong softening of the shear modulus C6667 stimulate theoretical studies of the orbital-fluctuation-mediated superconductivity, which favor the s++ state without sign change8910.

In contrast to the full-gap superconductivity in most of the iron-based superconductors, some systems show signatures of line nodes in the SC gap. While most of the nodal SC compounds such as KFe2As21112 show low Tc < 10 K, BaFe2(As1-xPx)2131415 has a relatively high Tc (~30 K) and is a suitable system for this purpose. In an angle-resolved thermal conductivity measurement16, four-fold symmetry as a function of magnetic field direction has been observed in the vortex state, suggestive of loop-like line nodes on the electron FS1718.

Angle-resolved photoemission spectroscopy (ARPES) is the most direct and powerful technique to unambiguously determine the location of line nodes in momentum space. For example, “octet line nodes” in KFe2As2 has been recently reported12. In BaFe2(As1-xPx)2, laser ARPES studies1920 have revealed nearly isotropic and FS-independent superconducting gaps on the hole FSs around the Z point, indicating the importance of orbital fluctuations in the pairing mechanism8910. However, in a recent study using synchrotron radiation by Zhang et al.21, a “horizontal line node”2223 has been observed on the outer hole FS around the Z point. Because no in-plane anisotropy was found in both ARPES results1921, the fourfold symmetry of the thermal conductivity16 remains to be explained.

In this study, in order to resolve this controversy, we have performed an ARPES study of BaFe2(As1-xPx)2 and clarified that there is no horizontal node on the hole FSs and the SC gaps are isotropic for all kz's, consistent with the laser ARPES study1920. Furthermore, we have revealed that gap nodes or at least strong anisotropy exists on the inner electron FS, which enables us to understand the fourfold symmetry in the thermal conductivity16. We have shown that a theoretical model including not only spin fluctuations but also orbital fluctuations well reproduces the observed SC gap structure, suggestive of a pairing mechanism beyond spin fluctuations.

Results

Energy gaps of the hole Fermi surfaces

Energy gaps of the hole FSs for BaFe2(As1-P)2 (x = 0.30, Tc = 30 K) around the Z point2021 are presented in Fig. 1. We observed at least two hole dispersions, implying that two out of the three bands are nearly degenerated as in the previous studies192124. The spectra at T = 15 K show a dip at EF for both bands, indicating a clear gap opening. The temperature dependence of the energy distribution curves (EDCs) at the Fermi momentum kF [Figs. 1(c1), 1(c2)] shows a clear gap opening even slightly above Tc, unlike the previous result21.

Figure 1

Superconducting gap observed on the hole FSs in BaFe2(As1-xPx)2 (x = 0.30, Tc = 30 K) around the Z point (hν = 35 eV).

(a) Temperature dependence of the symmetrized ARPES spectra in the k direction taken with a circularly polarized light. Fermi momentum kF's are indicated by arrows in the data taken at T = 100 K. (b) Symmetrized ARPES spectra in the kX direction (cut 3) with a linearly polarized light. The intensity of the outer hole band is enhanced due to matrix-element effect. (c1,c2) EDCs at kF for the outer and inner hole FSs. (d1)-(d3) Temperature dependence of the EDC at kF above and below Tc for cut 3 in panel (b). The EDCs in panel (d1) are symmetrized in panel (d2). The spectrum in panel (d3) has been obtained by dividing the spectrum below Tc by that above Tc in panel (d2). (e) Symmetrized EDCs corresponding to the kF points in panel (b). Vertical bars indicate shoulders in the low temperature spectra, indicating a superconducting gap. (Inset) Sizes of the gaps are plotted as a function of Fermi surface angle θFS.

We have also investigated the gap anisotropy of the hole FSs [Fig. 1(e)]. In Figs. 1(d1)–1(d3), we show an example of the EDC at kF below and above Tc. The symmetrized EDC below Tc have been divided by those above Tc and we obtain peak structure at ~6 meV [Fig. 1(d3)]. Since this structure evolves at low temperature as a shoulder in the EDCs [Fig. 1(d1)], we attributed this peak to a SC peak. Similar shoulders are observed at various kF points on the outer hole FS [Fig. 1(e)] and their energies are nearly isotropic, consistent with the laser ARPES result19. Thus, the four-fold oscillation in the angle-resolved thermal conductivity measurements16 is hardly explained by the isotropic character of the outer hole band.

Next, we present ARPES spectra of the hole FSs with various photon energies and hence for various kz's as shown in Fig. 2. The photon energies hν ~ 23 eV and ~35 eV correspond to the kz of the Γ and Z points, respectively [Fig. 2(d)]. Three hole dispersions are clearly resolved near the Γ point [Fig. 2(e)]. For the β and γ FSs [Figs. 2(b) and 2(c)], the gap energies are ~5–8 meV and are nearly independent of photon energy, i.e., independent of kz. For the α and β bands [Figs. 2(a) and 2(b)], the EDCs around the Z point (~35 eV) show a hump (at ~12–18 meV) with a shoulder (at ~7 meV). While the shoulder signifies a superconducting gap as in Fig. 1, the humps for the α and β FSs indicate a pseudogap2526. The SC gap is nearly independent of hν [panel (f)] and, hence, the hole FSs do not have an horizontal line node at any kz.

Figure 2

Superconducting gap observed on the hole FSs with various kz in BaFe2(As1-xPx)2 (x = 0.30, Tc = 30 K).

(a–c) Symmetrized EDCs at kF points in the Γ-X direction taken below Tc. Vertical bars indicate the gap energy. (d) Correspondence between the incident photon energy, kz, and the three-dimensional hole FSs (blue curves). (e) Second derivative plots of the ARPES spectra around the Γ point. (f) Gaps estimated in panels a–c are plotted as a function of hν.

Energy gaps of the electron Fermi surfaces

In order to investigate the possible existence of line nodes on the electron FSs, a photon energy of hν = 40 eV with a circularly polarized light was used as shown in Fig. 3, because with this polarization signals from the inner and outer electron FSs can be distinguished due to matrix element effects as shown in panel (a). In the inner electron FS [Fig. 3(b)], while the EDC at the Fermi surface angle θFS = 80° shows a clear shift (~5 meV) from EF, the shift of the EDC at θFS = 170° is smaller (<~2 meV), indicating a strong anisotropy of the superconducting gap.

Figure 3

Superconducting gap anisotropy observed on the electron FSs around the X point in BaFe2(As1-xPx)2 (x = 0.30, Tc = 30 K) taken at hν = 40 eV.

(a) Fermi surface mapping using a circularly polarized light. The Fermi angle is defined so that the direction from X to Γ is θFS = 0. (b) EDCs at kF taken below Tc (T = 13 K) and compared with gold spectra. (c) (d) EDCs at kF taken below (T = 13 K) and above (T = 35 K) Tc for the inner and outer FSs. Vertical bars indicate the peak positions and the crossing energy between the spectra below and above Tc. (e) (f) Energy of the peak and the crossing point for the inner and outer FSs are plotted as a function of Fermi surface angle θFS. While the SC gap of the inner FS is highly anisotropic, a clear anisotropy is not identified in the outer FS. We could not obtain the signal of the outer band near the edge of the FS because its intensity is weak and merges with the inner band.

As in panel (b), the leading edge of the spectrum is useful to detect the gap anisotropy. Therefore, the crossing point between the EDCs below and above Tc [Figs. 3(c) and 3(d)] will reflect the magnitude of the SC gap. Also, we have determined the energy of SC peak in the same manner as in Fig. 1(d1)–(d3). In Figs. 3(e) and 3(f), the SC gap magnitudes estimated from the crossing point and the peak energy are plotted as a function of θFS. These plots indicate that the inner FS has a gap minimum near the edge of the FS (θFS ~ 0 or 180°). We have also confirmed this strongly anisotropic SC gap for the inner electron FS with several experimental conditions. (See Supplementary Information, Figs. S2 and S3.) Although the minimum gap value in the inner FS appears to be finite, it should be remembered that ARPES has finite kz resolution (inverse of the photoelectron mean-free-path ~0.5 nm). If the line nodes are distributed in a three dimensional shape such as a loop-like node171927, kF's with finite gaps inevitably contribute to EDCs and the gap would look finite.

Discussion

Here, we illustrate a possible momentum dependence of the SC gap function from the present ARPES study in Fig. 4(a). The outer hole FS near the Z point does not show a signature of vertical nor horizontal line nodes. In contrast to the isotropic gap on the hole FSs, the gap minimum has been observed on the inner electron FS at the longer edge of the ellipsoid-shaped FS cross-section [Fig. 3 and Fig. 4]. Khodas and Chubukov31 have shown the folded model of the electron pockets and deduced vertical loop-like nodes in the electron FSs. Even if this is the case, it is still difficult to reproduce the loop-like node if there are three hole FSs as in the present results28. Thus, the observed momentum dependence of the SC gap magnitude is difficult to understand from the spin-fluctuation-mediated mechanism alone. The comparable sizes of the SC gaps of the three hole FSs, that is, for FSs of different orbital character indicate that the inter-orbital scattering is required for the Cooper pair formation8910. Also, the disappearance of the xy hole FS is required in the spin-fluctuation-mediated mechanism to achieve a strongly anisotropic gap or line nodes in the electron FSs227, while we have clearly observed three hole bands including the xy hole FS around the Γ point (Fig. 2).

Figure 4

SC gap Δ for the FSs of BaFe2(As1-xPx)2.

(a) Momentum dependence of the Δ for x = 0.30 deduced from the present ARPES result. The color scale represents the magnitude of the SC gap. Loop-like nodes or gap minima appear near the rim of the inner electron FSs. (b) Theoretical calculation of the anisotropy for inner electron FS with orbital fluctuations in ref. 28. The green lines represent the gap nodes.

The three-dimensional gap structure in ref. 28 obtained by a model calculation including orbital fluctuations, shown in Fig. 4(b), shows common features with the experimental results of the hole and electron FSs. In this model, when the inter-orbital scattering is moderately strong, the highly anisotropic gap of the electron FS is expected to have nodes in the crossover region between the s± and s++-wave superconductivity. According to the calculated results28, when a loop-like node appears at the longer edge of the electron FSs, a large part of the FS has an order parameter of opposite sign to that of the hole FSs. Thus, the present observation of the gap anisotropy in the electron FS indicates the realization of nearly s±-wave SC state.

The present result on the SC gap of the hole FSs for the x = 0.30 sample described above have been qualitatively reproduced for a slightly overdoped x = 0.38 sample as shown in Supplementary Fig. S4 and, therefore, can be considered as robust features. Also, in the present study, while the two electron FSs have gap values ~8–10 meV, the hole FSs show relatively small values ~5–8 meV. This can be contrasted with the previous ARPES study of Ref. 21, which shows similar gap values between electron and hole FSs except around the Z point. Here, we discuss possible origins of the discrepancy in the SC gap anisotropy with the previous study by Zhang et al.21. We should note that the samples were grown by the self-flux method in our study while a flux-free method was applied in Ref. 21. In the process of the sample growth, starting compounds are different between these methods. Therefore, we speculate that such a difference in the sample growth may give differences in the local structure and/or unknown defects, hence, the detailed electronic structure.

In the present study, the strongly anisotropic SC gap and the absence of a horizontal node are suggestive of the mechanism beyond spin fluctuations such as orbital fluctuations. As a possible origin, inter-orbital interaction, electron-phonon interaction8, and vertex correction of the Coulomb interaction29 have been discussed so far. Since these interactions may depend on the doping level and material families, the pairing mechanism beyond spin fluctuations should be revealed in future systematic studies of the SC gap in various kinds of the iron pnictide superconductors.

Methods

Single crystals of BaFe2(As1-xPx)2 with x = 0.30 (Tc = 30 K) were grown by a self-flux method30. The details of the sample growth, characterization are described in Supplementary S1. ARPES experiments were carried out at BL 9A of Hiroshima Synchrotron Radiation Center (HiSOR) and BL-28A of Photon Factory (PF). At HiSOR BL 9A, a Scienta SES-R4000 analyzer and a circularly-polarized light were used with the total energy resolution of ~7–8 meV. At PF BL-28A, a Scienta SES-2002 analyzer and a circularly- and linearly-polarized light were used with the total energy resolution of ~8–10 meV. The crystals were cleaved in situ at T = 8–13 K in an ultra-high vacuum of ~5 × 10−11 Torr. Calibration of the Fermi level (EF) of the samples was achieved by referring to that of gold. In-plane (kx, ky) and out-of-plane electron momenta (kz) are expressed in units of π/a and 2π/c, respectively, where a = 3.92 Å and c = 12.8 Å are the in-plane and the out-of-plane lattice constants. Here, the x and y axes point towards nearest neighbor Fe atoms. The correspondence between kz and hν has been determined in our previous ARPES studies2024.

Author Contributions

T.Y., S.I., T. Shimojima, W.M., K.S., H.S. and I.N. performed ARPES experiments. T.Y. and S.I. analyzed the ARPES data. S.K. and M.N. synthesized single crystals. K.I., S.S., Y.N., H.A., M.A., A.I., H.N., M.T., H. Kumigashira and K.O. supported synchrotron ARPES experiments. T. Shibauchi, T.T. and Y.M. supported growing single crystals at Kyoto University. S.U., Y.T., T.I., K.K., C.H.L., A.I. and H.E. supported growing single crystals at AIST. H.I., R.A., T.S., S.O. and H. Kontani are responsible for theoretical part of the project. T.Y. and A.F. designed the project and wrote the manuscript with suggestions by T. Shibauchi, Y.M., S.U., H.I., R.A. and H. Kontani and all other coauthors.