Main

The pairing symmetry of the Cooper pair in a superconductor is manifested in an energy gap of its single-particle excitation spectrum. In particular, nodes (that is zero gaps) or line nodes of the superconducting gap often imply unconventional pairing symmetries. For most iron-based superconductors, there are electron Fermi surfaces (FSs) at the Brillouin zone corner and hole FSs at the zone centre. It has been proposed that the pairing interactions between the electron and hole FSs will induce a nodeless s-wave order parameter with opposite signs on them13,14,15. Whereas this nodeless s±-wave pairing symmetry has gained increasing experimental support for some compounds16,17,18, an increasing number of reports on the nodal gap of others pose serious challenges5,6,7,8,9,10,11,12 and debates19,20,21,22,23,24,25. So far, the key to resolving this issue, namely the location of the nodal gap, remains unknown.

We have made angle-resolved photoemission spectroscopy (ARPES) measurements on BaFe2(As0.7P0.3)2 with a superconducting transition temperature (Tc) of 30 K (Methods). As previous detailed polarization-dependent study has shown26 and as reproduced in Fig. 1a, there are three hole FSs (α, β and γ) surrounding the central Γ–Z axis of the Brillouin zone, and two electron FSs (δ and η) around the corner. Near Γ, the α and β FSs are coincident, and they are mainly composed of Fe dx z and dy z orbitals. The γ band is composed of the dx y orbital, and shows little kzdispersion26. The αFS exhibits a large warping along kz, and becomes the outmost FS around Z (refs 26, 27). To examine the superconducting gap, Fig. 1b shows the symmetrized photoemission intensity in the normal and superconducting state taken along cut 1 across Γ. The temperature-broadening effect of the Fermi–Dirac distribution on the spectrum is minimized by symmetrizing. The spectral weight near the Fermi energy (EF) is suppressed in the superconducting state. More specifically, the temperature dependences of the symmetrized photoemission spectra at the Fermi crossings of the α/β and γ bands are shown in Fig. 1c. Above Tc the spectral lineshape does not change noticeably, but below Tc the spectral weight near EF is suppressed quickly because of the opening of a superconducting gap with decreasing temperature. A small coherent peak can be observed at 8 K. By fitting the spectra with a typical superconducting-state spectral function (Fig. 1c), we could obtain the temperature dependence of the superconducting gap in Fig. 1d, which can be fitted well to the Bardeen–Cooper–Schrieffer formula (solid line). Similarly, the opening of the gap on the δ and η FSs is illustrated in Fig. 1e–g for kz = 0.54π. The extrapolated zero-temperature gaps give 2Δ0/kBTc≈5–6 for BaFe2(As0.7P0.3)2.

Figure 1: The temperature dependence of the photoemission data of BaFe2(As0.7P0.3)2.
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a, The three-dimensional FSs of BaFe2(As0.7P0.3)2. The two-iron unit cell is implemented here, with the Fe–Fe direction as the kx direction. The electron FSs are only illustrated at one corner of the Brillouin zone for simplicity. b, The photoemission intensity taken around the zone centre with 22 eV photons at 41 and 8 K. c, The temperature dependence of the symmetrized spectra measured at the Fermi crossings of α/β and γ along the cut in b. Two examples of the fitted curve, background and superconducting spectral function are shown with black dashed lines, dotted lines and solid lines respectively. d, The temperature dependence of the superconducting gaps of the α/β and γ bands. The gap size is estimated by fitting the symmetrized spectra as described in Supplementary Section S3. e–g, The same as b–d, but taken around the zone corner along cut 2 with 22 eV photons. The error bars in d and g are standard deviations of the measured superconducting gaps.

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Figure 2 presents an extensive survey on the possible gap nodes on electron FSs following the proposal of a recent angle-dependent transport study7. Figure 2a shows four typical cuts in the kz = 0.5π plane. The isotropic superconducting gaps open on all the Fermi crossings. Similar data are measured for different kz values. The superconducting-state spectra are shown in Fig. 2b along three cross-sections of the η FS in kz = 0, 0.5π and π planes, and in Fig. 2c for its kz–ky cross-section. The leading-edge gap opening can be clearly observed with little kz dependence from the raw spectra in Fig. 2d. Similarly, Fig. 2d–f plot the spectra on the δFS. In addition, the data taken in the kz = 0.2π, 0.34π, 0.54π, 0.64π and 0.8π planes are shown in Supplementary Fig. S5. The superconducting gaps are always finite in all cases. If the gap nodes were continuously located along certain vertical lines or loops on the FS as suggested7,19,20,21, they should not be missed in such an extensive search. We would have observed at least some variation of the gap if not nodes, owing to the finite momentum resolution. The fact that the superconducting gap is finite and almost fixed to the same size over the entire δ (or η) FS proves that the line nodes of the gap are absent from the electron FSs.

Figure 2: The superconducting-gap distribution on the electron FSs of BaFe2(As0.7P0.3)2.
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a, The photoemission intensities taken along four momentum cuts near the zone corner with 22.5 eV photons. b, The symmetrized spectra at the marked polar angles on the ηelectron FS measured at three typical kz values with 27, 22.5 and 18 eV photons. c, kz dependence of the symmetrized spectra measured on the η electron FS. d, kz dependence of the raw spectra measured on the δ and η electron FSs. The black dotted curves are reference spectra from a piece of polycrystalline gold in electrical contact with the sample. e,f, The same as b,c, but taken on the δ electron FS. The dashed curves in b, c, e and f are guides to the eyes for the variation of the superconducting gap. Hereafter, the momentum location of each spectrum is denoted by either the polar angle θ as defined in the insets, or a solid circle on the FS. All data were taken in the superconducting state at 9 K.

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It was predicted that sufficient phosphorus doping in BaFe2(As1−xPx)2 would shift the dx y-based γ band below EF, and consequently vertical line nodes would appear in the electron FS (refs 19, 20, 21). The fact that γ does not sink below EF, and the absence of vertical nodes on the electron FSs, all indicate that this is not the case.

Figure 3 gives the detailed map of superconducting gaps on the hole FSs. The symmetrized spectra for different kz values along the β, γ and α FSs are shown in Fig. 3a–c respectively. As indicated by the dashed line, the gap decreases slightly from kz=0 to kz=π on β and γ, but much more remarkably on α, and it even closes near the Z point. The nodal superconducting gap on the α FS around Z is further confirmed by the vanishing leading-edge gap in the corresponding spectra presented in Fig. 3d and Supplementary Fig. S4. On the other hand, the middle points of the spectral leading edges are always below EF for the β and γ bands, indicating their nodeless nature. The photoemission intensity along three cuts (Fig. 3e) and the symmetrized spectra around three FS cross-sections (Fig. 3f) in the kz=π plane show that finite and isotropic gaps open on the β and γ FSs, and a circular line node exists around Z on the α FS. As a comparison, the data taken in the kz=0(Supplementary Fig. S6) and kz=0.38π planes show a full gap for all three FSs (Fig. 3g,h). Such a horizontal line-node distribution immediately rules out the d-wave pairing symmetry, which would give four vertical line nodes in the diagonal directions (θ=±45°, ±135°), as in the cuprates. Of note, a recent ARPES study with a 7 eV laser on BaFe2(As0.65P0.35)2 has claimed the absence of a nodal gap around Z (ref. 28). However, on the basis of our extensive photon-energy-dependence study, a 7 eV photon actually measures the region with kz=0.34π, far from Z.

Figure 3: The superconducting-gap distribution on the hole FSs of BaFe2(As0.7P0.3)2.
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a–c, kz dependence of the symmetrized spectra measured on the β, γ and α hole FSs respectively. The symmetrized spectra near kz=0 and kz=π are shown in thicker curves. The dashed line is a guide to the eyes for the variation of the superconducting gap at different kz values. d, kz dependence of the raw spectra measured on the β, γ, and α hole FSs. The black dotted curves are reference spectra from a piece of polycrystalline gold in electrical contact with the sample. The leading-edge middle point only crosses EF near Z for the α band, as illustrated by the black arrow. Note that, as the leading-edge middle-point position underestimates the gap, the gap magnitudes were determined through the fitting procedure described in Supplementary Section S3. e, The photoemission intensities taken along three momentum cuts, and f, the symmetrized spectra at the marked polar angles along the α, β and γ hole FSs taken with 35 eV photons in the kz=π plane around Z. g,h, Similar to e,f, but taken with 27 eV photons in the kz=0.38π plane. All data were taken in the superconducting state at 9 K. We note that we can usually distinguish an energy gap if it is bigger than 20% of the resolution in a photoemission experiment, and the energy resolution here with 35 eV photons is 6 meV.

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The gap distribution of BaFe2(As0.7P0.3)2 is summarized in Fig. 4a, together with that of Ba0.6K0.4Fe2As2 replicated from ref. 29 for comparison. The limited nodal region of BaFe2(As0.7P0.3)2 explains its relatively high Tc. The gaps on the α, β, γ and δ FSs vary noticeably with kz in BaFe2(As0.7P0.3)2, whereas only the gap on the α FS exhibits significant kz dependence in Ba0.6K0.4Fe2As2. Figure 4b plots the gap of BaFe2(As0.7P0.3)2 as a function of |cos(kxa)cos(kya)|. There are obvious deviations from the predicted gap function of Δ0|cos(kxa)cos(kya)| of the s±-wave pairing symmetry based on a two-dimensional model13,14,15,16. Furthermore, the superconducting gaps on all FSs of BaFe2(As0.7P0.3)2 and the α FS of Ba0.6K0.4Fe2As2 are plotted in Fig. 4c–e as functions of kz, and fitted to a phenomenological function: Δ1|cos(kxa)cos(kya)|+Δ2cos(kzc) (ref. 22). The extra term here is the kz suppression of the superconducting gap, which could refer to the interlayer coupling in an anisotropic layered superconductor or an orbital-dependent pairing mechanism22,24,25,29. With different Δ1 and Δ2 for each band, the gaps of all the nodeless bands, including the α band of Ba0.6K0.4Fe2As2, could be fitted. However, the nodes and gap suppression on the α FS in BaFe2(As0.7P0.3)2 cannot be fitted well by such a formula, probably owing to the strong mixing of another orbital as discussed below.

Figure 4: Momentum dependence of the superconducting gap.
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a, False-colour plots of the gap distribution on the FSs of BaFe2(As0.7P0.3)2 and Ba0.6K0.4Fe2As2. b The superconducting gap of BaFe2(As0.7P0.3)2 versus |cos(kxa)cos(kya)|. c,d, The superconducting gaps on the δ and ηelectron FSs (c) and on the α, β and γ hole FSs (d) for BaFe2(As0.7P0.3)2 as functions of kz. The solid lines are fits to Δ1|cos(kxa)cos(kya)|+Δ2cos(kzc). e, The superconducting gap on the α FS of Ba0.6K0.4Fe2As2 as a function of kz. The error bars in b–e are standard deviations of the measured superconducting gaps. f, The band structure of BaFe2(As0.7P0.3)2 near Γ and Z. The ellipses indicate the spectral weight of the ζ band.

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There have been a few theoretical predictions on possible nodes near Z in the hole FS with strong d 3 z 2 − r 2 orbital characters in iron pnictides22,23,24,25. In particular, our findings qualitatively agree with the calculations of ref. 24 on BaFe2(As1−xPx)2. Those authors found that, with increasing phosphorus concentration, the d 3 z 2 − r 2 orbital would be strongly mixed into the α band near Z. As a result, the superconducting gap could reverse sign on the α FS in the vicinity of Z, and thus a nodal circle emerges at the location where the sign is switched. Indeed, as pointed out in a previous study26, and also illustrated in Fig. 4f, we do find that the ζ band with strong d 3 z 2 − r 2 orbital character comes across the αband, and the Fermi crossing of αis much closer to the top of the ζ band near Z than near Γ, which would mix a significant amount of the d 3 z 2 − r 2 orbital into α near EF (more details and polarization-dependent ARPES evidence for this are presented in Supplementary Section S6). This makes sense of the intriguing observation that nodes appear in iron pnictides when the distance between the pnictogen and Fe plane (hP n) is less than 1.33 Å (ref. 9). As for BaFe2(As1−xPx)2, hP n is reduced by phosphorus doping, and it would cause larger kz dispersion and strong mixing of the d 3 z 2 − r 2 orbital into α.

The horizontal ring node around Z in BaFe2(As0.7P0.3)2 is not forced by symmetry, as it is fully symmetric with respect to the point group. Therefore, it is an ‘accidental’ one, which is probably induced by the strong three-dimensional nature of the αband, for example its sizable d 3 z 2 − r 2 orbital character near Z. As the superconducting order parameters at kz=0 and kz=2π should have the same sign, the sign of the gap function would reverse twice near Z instead of just once at kz=π. Consequently, there should be two circular nodes located symmetrically with respect to Z (refs 24, 25). With limited momentum resolution along kz, we could not resolve such details of the nodal gap structure at present. However, it is possible that, with increasing kz dependence at higher phosphorus doping, these two ring nodes could be further separated, and thus resolved.

Methods

High-quality single crystals with nominal composition BaFe2(As0.7P0.3)2 were synthesized through flux-free crucible growth. Shiny platelet crystals as large as 2×2×0.05 mm3were obtained, which exhibit a Tc of 30 K and a residual resistivity ratio of about 10 (see Supplementary Section S1 for details). Data were taken at beamline 5-4 of Stanford Synchrotron Radiation Lightsource (SSRL). All the data were taken with a Scienta electron analyser; the overall energy resolution was 5–8 meV depending on the photon energy and the angular resolution was 0.3°. The samples were cleaved in situ, and measured under ultrahigh vacuum of 5×10−11 torr. The out-of-plane momentum kz is calculated and folded into the upper half of the first Brillouin zone as described in Supplementary Section S2. It is denoted in the unit of 1/c′, where c′ is the distance between two neighbouring FeAs layers, which is half of the out-of-plane lattice constant c.