Revealing the intrinsic superconducting gap anisotropy in surface-neutralized BaFe$_2$(As$_{0.7}$P$_{0.3}$)$_2$

Alkaline-earth iron arsenide (122) is one of the most studied families of iron-based superconductors, especially for angle-resolved photoemission spectroscopy. While extensive photoemission results have been obtained, the surface complexity of 122 caused by its charge-non-neutral surface is rarely considered. Here, we show that the surface of 122 can be neutralized by potassium deposition. In potassium-coated BaFe$_2$(As$_{0.7}$P$_{0.3}$)$_2$, the surface-induced spectral broadening is strongly suppressed, and hence the coherent spectra that reflect the intrinsic bulk electronic state recover. This enables the measuring of superconducting gap with unpreceded precision. The result shows the existence of two pairing channels. While the gap anisotropy on the outer hole/electron pockets can be well fitted using an s$_\pm$ gap function, the gap anisotropy on the inner hole/electron shows a clear deviation. Our results provide quantitative constraints for refining theoretical models and also demonstrate an experimental method for revealing the intrinsic electronic properties of 122 in future studies.


Introduction
After the discovery of superconductivity in LaO1-xFxFeAs (1111), many families of iron-based superconductor have been found, including iron-selenide (11), alkaline iron arsenide (111), alkaline-earth iron arsenide (122), etc 1,2 . Among them, the 122 family is the most studied family of iron-based superconductors, due to its high sample quality, high superconducting transition temperature (Tc), tunable carrier density, and diversity of compounds with different chemical substitutions. However, aside from these advantages, the lattice structure of 122 contains a single alkaline-earth-metal plane and hence has no charge-neutral cleavage surface (Fig. 1a,b). In BaFe2(As1-xPx)2, for example, half Ba ions are removed at the cleaved surface, and the residual Ba ions distribute inhomogeneously, forming various surface terminations [3][4][5][6][7] . While the alkaline-earth-metal-terminated and arsenic-terminated surfaces have been observed by scanning tunneling microscopy (STM) [4][5][6][7] , the alkaline-earth-metaldeficient surface also exists with a reconstruction of alkaline-earth-metal atoms with 1×2 and √2×√2 periods , 6,7 . In bulk materials, one alkaline-earth-metal plane donates two electrons to the two nearest Fe-As/P planes. However, at the surface, the number of charge that transfers to the topmost Fe-As/P plane varies strongly depending on the concentration Here, we report the measurement of gap anisotropy in an optimal-doped 122 compound BaFe2(As0.7P0.3)2 utilizing ARPES and in-situ potassium deposition. We find that by depositing a small amount of potassium on the sample surface, the spectra become sharp and coherent, which allows us to measure the superconducting gap anisotropy on all Fermi surface sheets with unpreceded precision. We show that the obtained gap anisotropy cannot be fitted using a single |cosk x cosk y | gap function, but could be explained by the nesting-and orbital-selectivity of the superconducting pairing. Our detailed and precise gap measurement provide crucial clues for uncovering the paring mechanism of iron-based superconductors. It also implies that the surface complexity of 122 need to be seriously considered. The potassium deposition can be used as a practical experiment method for revealing the intrinsic electron structure and gap anisotropy of 122 iron-based superconductors in the future studies. Note that, the large hole pocket (αZ) is a shadow Fermi pocket that is folded from the Z point due to the finite k z resolution of ARPES 17 .  To further show the effect of potassium deposition, we take the energy-momentum cuts across the hole/electron pockets and plot their doping dependence in Fig. 2. Around the Γ point, the spectra become sharper with potassium deposition (Fig. 2a), and meanwhile the superconducting peaks become more coherent (Fig. 2b). Around the M point, a surface band could be observed at around -20 meV as pointed out by the white arrow (Fig. 2c).
With potassium deposition, this surface band weakens and eventually diminishes. As a result, the superconducting coherent peak is clearly resolved (Fig. 2d). It should be noted that, we could not resolve any change of Fermi crossings (kFs) and gap magnitudes (∆), which indicates that the total potassium coverage is very low. Based on our energy and momentum resolutions, we could set an upper bound of total potassium coverage to be ~0.015 ML. For each doping step, the increment of potassium coverage is estimated to be below 0.005 ML. Such small amount of potassium is sufficient to improve the spectral quality while having little influence on band structure and superconductivity. The red arrow illustrates the direction of the data presentation. b The merged image of the symmetrized EDCs for better visualizing the gap anisotropy. The polar angle (θ) is defined in a. c, d, e, f, g, and h are the same as a and b, but taken on the β, δ, and η pockets respectively. All data were taken in the D3 sample at 8 K.
Superconducting gap anisotropy in potassium-coated BaFe2(As0.7P0.3)2. Being able to resolve the intrinsic ARPES spectra is critical for the quantitative spectra analysis. The sharpness of spectra taken in potassium-coated BaFe2(As0.7P0.3)2 is now comparable with that taken in 11 and 111 iron-based superconductors [21][22][23][24][25] (Supplementary Fig. 1). On one hand, the effective mass and lifetime of quasiparticles could be determined more accurately, which is important for studying the quantum critical phenomena of BaFe2(As1-xPx)2 26,27 . On the other hand, the superconducting coherent peaks are well defined on all Fermi surface sheets, which allows us to measure the superconducting gap anisotropy with unpreceded precision. The results are shown in Fig. 3. The superconducting gap is nearly isotropic on the α and β hole pockets (∆ α and ∆ β ) (Fig. 3a-d), but shows moderate anisotropy on the δ and η electron pockets (∆ δ and ∆ η ) (Fig. 3e-h). For ∆ δ , the gap reaches maximum at 90°, while for ∆ η , the gap maxima locate at 45° and 135°.  Here, our detailed and precise gap measurements allow us to test the validity of s ± gap function quantitatively. We fitted the data using the experimental determined Fermi surface ( Fig. 4a) and summarized the fitting results in Fig. 4b-f. For the superconducting gap anisotropies on the β and η pockets, the four-fold symmetry of ∆ η and the relative gap magnitudes of ∆ β and ∆ η can be well described by the s± gap function with ∆0 = 8.7 meV.
However, for the α and δ pockets, the superconducting gap clearly deviates from the s± gap function with a larger gap magnitude, which indicates a stronger superconducting pairing on the α and δ pockets.

Discussion
We first discuss how the potassium atoms play roles on the surface of BaFe2(As1-xPx)2.
There are several possible scenarios. First, electrons transfer from the potassium atoms to the sample surface, which neutralizes the charge-non-neutral surface, leading to a suppression of the surface broadening effect. Second, the potassium atoms could act as a catalyzer which causes the redistribution of alkaline-earth metal atoms on the sample surface in a more homogeneous way. Third, the potassium atoms scatter electrons at the sample surface. The surface electronic states then turn into an incoherent and continuous background that is inconspicuous in photoemission spectra. To understand the mechanism of potassium deposition, further experimental and theoretical studies are required.
Nevertheless, our results highlight the surface complexity of 122 iron-based superconductors. This implies that previous photoemission results taken on 122 should be carefully revisited.
Moreover, ARPES data taken on BaFe2As2, SrFe2As2, CaFe2As2, etc [38][39][40] show complex band structures. The number of bands observed by ARPES is inconsistent with the band calculations. Here, we show that the surface complexity might explain these controversial behaviors of 122 iron-based superconductors. The possible existence of surface-related features could be easily verified using potassium deposition. For BaFe2(As1-xPx)2, its nodal location is still under debates 18,28,29,41 . We measured the kz dependence of superconducting gap in the D3 sample ( Supplementary Fig. 2). While our high-quality data confirm the existence of gap nodes on the hole pockets around the Z point 18 , no gap node is resolved on the electron pockets. Although we cannot fully exclude the possible existence of nodal loop on electron pockets due to our finite kz resolution, we show that the data quality can be significantly improved by potassium deposition especially for the gap measurement on the electron pockets. With a more bulk-sensitive and comprehensive photon energy dependent experiment, it can be determined whether the nodal loop exists or not.
We now turn to the in-plane superconducting gap anisotropy, which has been studied by ARPES for many iron-based superconductors. For 111 and 11 compounds, such as LiFeAs, NaFe1-xCoxAs and FeSe, the Fermi pockets are small and the Tcs are relatively low, making the gap function fitting unreliable and unable to provide effective information 8,[23][24][25] . For 122 compounds, due to the surface broadening effect, the superconducting gap anisotropy, especially the gap anisotropy on the electron pockets, has never been resolved clearly.
Here, we achieve an accurate and reliable gap measurement of 122 using potassium- The intra-orbital pair scattering could also lead to a separation of two pairing channels respectively from the d xz /d yz and d xy orbitals. Based on above discussions, our results indicate that the intra-orbital pair scattering between two nested Fermi pockets play a dominating role in the superconducting pairing of iron-based superconductors. As a result, the superconducting pairing becomes nesting-and orbital-selective 42,43 . By fitting the gap anisotropy using a more complex and parameterized gap function, the detailed momentum and orbital dependence of pairing interactions could be obtained, which would help to construct an accurate and realistic superconducting pairing model for iron-based superconductors.
In summary, we report the superconducting gap measurement in potassium-coated BaFe2(As0.7P0.3)2. We found that a small amount of potassium deposition could suppress the surface-broadening effect and help us to reveal the intrinsic electron structure of BaFe2(As0.7P0.3)2. Our high quality and precise gap measurement distinguishes two pairing channels, which unveils the nesting-and orbital-selective nature of the superconducting pairing of iron-based superconductors. Our results show that the surface-neutralization enables the photoemission data taken in 122 to be analyzed with unpreceded precision.
The results would provide crucial clues for uncovering the pairing mechanism of iron-based superconductors.

Methods
Sample preparations. High quality BaFe2(As0.7P0.3)2 single crystals were grown using selfflux method 44 . Ba2As3, Ba2P3, FeAs, FeP were starting materials, which were mixed at a molar ratio of 2.82 : 0.18 : 0.94 : 0.06, placed in an Al2O3 crucible, and sealed in an iron crucible. The crucible was heated at 1150 ℃ for 10 hours, and then the temperature cooled down to 900 ℃ at a rate of 1 ℃ per hour. Finally, 1 mm × 1 mm × 0.2 mm highquality single crystal can be obtained. The Tc is around 30 K as confirmed by magnetic susceptibility measurement.
Angle-resolved photoemission spectroscopy. The ARPES data were taken at Stanford synchrotron radiation lightsource (SSRL) beamline 5-4. The photon energy is 23 eV. The overall energy resolution is around 5 meV and the angular resolution is around 0.3°. The samples were cleaved in-situ and measured in vacuum better than 5×10 -10 mbar. All data were measured at 8 K. The potassium deposition was conducted in-situ using a potassium dispenser. We repeated the deposition several times. The deposition sequence is denoted using Dn (n is the doping times). The current of the potassium dispenser is ~5.4 A, and each deposition last for ~8 seconds.

Data availability
Data that support the findings of this study are available upon reasonable request from the corresponding authors.