Single particle tunneling spectroscopy and superconducting gaps in layered iron based superconductor KCa_{2}Fe_{4}As_{4}F_{2}
Wen Duan, Kailun Chen, Wenshan Hong, Xiaoyu Chen, Huan Yang, Shiliang Li, Huiqian Luo, Hai-Hu Wen
aa r X i v : . [ c ond - m a t . s up r- c on ] F e b Single particle tunneling spectroscopy and superconducting gaps in layered iron basedsuperconductor KCa Fe As F Wen Duan, Kailun Chen, Wenshan Hong, , Xiaoyu Chen, Huan Yang, , ∗ Shiliang Li, , , Huiqian Luo, , and Hai-Hu Wen , † National Laboratory of Solid State Microstructures and Department of Physics,Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China Beijing National Laboratory for Condensed Matter Physics,Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China and Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, China
We perform scanning tunneling microscopy/spectroscopy study on the layered iron based super-conductor KCa Fe As F with a critical temperature of about 33.5 K. Two types of terminatedsurfaces are generally observed after cleaving the samples in vacuum. On one commonly obtainedsurface, we observe a full gap feature with energy gap values close to 4.6 meV. This type of spectrumshows a clean and uniform full gap in space, which indicates the absence of gap nodes in this super-conductor. Quasiparticle interference patterns have also been measured, which show no scatteringpatterns between the hole and tiny electron pockets, but rather an intra-band scattering pattern isobserved possibly due to the hole-like α pocket. The Fermi energy of this band is only about 24 ± ± . Fe As F , and the superfluid is mainly contributedby the hole-like Fermi surfaces near Γ point. This would inspire further consideration on the effectof the shallow and incipient bands near M point, and help to understand the pairing mechanism inthis highly layered iron-based superconductor. I. INTRODUCTION
Iron-based superconductors (FeSCs) are the secondfamily of unconventional high-temperature superconduc-tors. In most FeSCs, several Fe derivative d -bands crossthe Fermi energy forming the electron- and hole-likepockets. Meanwhile, band structures and Fermi surfacesare quite different in various FeSCs, and they are alsovery sensitive to chemical doping or external pressure.The widely accepted s ± pairing symmetry in some FeSCsis based on the nesting between hole pockets near Γ pointand electron pockets around M point with similar sizesbased on the weak coupling scenario, but the gap symme-try and the gap structure can be different in other FeSCsbecause of different structures of Fermi surfaces [1].The newly found A Ca Fe As F ( A = K, Rb, Cs) isa representative compound of the layered FeSCs, andthe critical temperature ( T c ) ranges from 28 to 33 K [2–4]. The crystal structure of KCa Fe As F (K12442) isshown in Fig. 1(a) as an example, one can see that inthese materials, double FeAs layers are separated by in-sulating Ca F layers. Such kind of layered structureresults in a significant anisotropy of superconductivityand normal-state resistance [4–7]. It is supposed thatthe 12442-type FeSCs have the intrinsic hole conductionwith the doping level of 0.25 hole/Fe. Interestingly, itis easy to transform the primary carrier from p -type to n -type by Co or Ni doping, but T c decreases with in- crease of the doped concentration of Co or Ni dopants[8, 9]. Meanwhile, T c can be slightly enhanced by apply-ing a hydrostatic pressure [10]. Transport measurementsin KCa Fe As F (K12442) single crystals suggest thatthe in-plane upper critical field is dominated by the Pauliparamagnetic effect instead of the orbital effect [11]. The-oretical calculation predicts that there are several holeand electron pockets in the K12442 [8, 12, 13]. Basedon a recent angle-resolved photoemission spectroscopy(ARPES) work conducted in K12442, three separate holepockets α , β , γ are observed around the Γ point, andone tiny electron pocket together with four incipient holebands (which barely touch the Fermi energy) are ob-served around the M point [14]. Obviously, this topol-ogy of Fermi surface cannot satisfy the nesting conditionbecause of very different sizes of hole and electron pock-ets. The nesting condition is satisfied by Co doping toK12442 with the doping level of about 0.1, but T c de-creases to about 25 K [8]. In this point of view, thesuperconductivity in 12442-type FeSCs may be differentfrom other FeSCs. ARPES measurements in K12442 ex-hibit six nodeless gaps with gap values ranging from 2meV to 8 meV for different Fermi pockets. The multi-ple and nodeless gap feature are also proved by differ-ent experimental methods [15, 16]. However, some otherworks claim that there might be line nodes on the su-perconducting gap(s) in 12442-type FeSCs [17–19]. Thecontroversies of the existence of gap nodes in 12442 sys-tem require further investigations. Although the nestingcondition is not satisfied in 12442-tpye FeSCs, the spinresonance peak is still observed around Q = (0 . , . s ± pairing sym-metry with the spin resonance can be explained in thestrong coupling approach with the absence of the nestingcondition [22]. In addition, the spin resonance mode witha downward dispersion is observed in K12442, and thiskind of dispersion is similar to the behavior in cuprates[20].In this paper, we report the experimental study onKCa Fe As F single crystals by the scanning tunnel-ing microscopy/spectroscopy (STM/STS). Fully gappedfeature is observed on almost all tunneling spectra. Wealso conduct the quasiparticle interference (QPI) mea-surements in the sample in order to obtain the informa-tion of Fermi pockets. Our results provide fruitful infor-mation to this multi-band superconductor. II. EXPERIMENTAL METHODS
FIG. 1. (a) Crystal structure of KCa Fe As F . (b) Temper-ature dependent magnetization measured in zero-field cooled(ZFC) and field-cooled (FC) processes under a magnetic fieldof 10 Oe. (c) Temperature dependence of normalized in-planeresistance measured at 0 T. The KCa Fe As F single crystals used in this workwere grown by the self-flux method [4]. Temperaturedependent magnetization and normalized resistance areshown in Figs. 1(b) and 1(c), and both of them show finesuperconducting transitions with critical temperature T c of about 33.5 K determined from the zero-resistance.STM/STS measurements were carried out in a scanning tunneling microscope (USM-1300, Unisoku Co., Ltd.).The K12442 samples were cleaved at about 77 K in an ul-trahigh vacuum with the base pressure of about 1 × − Torr, and then they were transferred to the microscopyhead which was kept at a low temperature. Electrochem-ically etched tungsten tips were used for STM/STS mea-surements after cleaning by the electron-beam heating.A typical lock-in technique was used in tunneling spec-trum measurements with an ac modulation of 0.1 mVand the frequency of 931.773 Hz. Voltage offsets werecarefully calibrated before STS measurements.
III. RESULTSA. Topography and tunneling spectra
Figure 2(a) shows a typical topographic image mea-sured on the surface of K12442 single crystal. Basedon the lattice structure of K12442, there are layers ofalkali-metal K atoms and those of alkaline-earth-metalCa atoms. The cleavage may occur in these layers withthe relatively weak bonding energy. After the cleavage,most probably, half K or Ca atoms remain in the surfacelayer of each separated part, which makes both surfaceunpolarized. This can get a proof from an atomicallyresolved topography shown in the upper-right inset inFig. 2(a) measured on a flat area far away from any de-fects. The topography shows a square lattice with thelattice constant of about 5.3 ˚A which is approximatelyequal to √ a = 3 .
87 ˚A). From the topographic image, one cansee that there are many hollows with different sizes onthe flat background. The depths of the hollows are from100 to 300 pm, and these hollows can be clearly seenfrom the re-scanned image shown in the lower-left insetin Fig. 2(a). Similar kinds of hollows have been observedin NaFe − x Co x As [23], LiFeAs [24], and RbFe As [25]but with much lower densities, and they may be the as-sembled vacancies of alkali metal atoms on the recon-structed surface. In Fig. 2(b), we show a typical tunnel-ing spectrum on the surface measured in a wide energywindow. The differential conductance is much larger innegative-bias side than that in positive-bias side, whichis consistent with the asymmetric density of states fromprevious band calculation results [12, 13]. FIG. 2. (a) A typical topographic image taken on a surfaceof K12442 measured at T = 1 . V set = 20 mV and I set = 200 pA. The inset in the upper-rightcorner shows the atomically resolved topography measured inanother flat area ( V set = 10 mV and I set = 500 pA). The in-set in the lower-left corner shows the re-scanned image with ahigher resolution of an area in (a) marked by the red dashedsquare ( V set = 20 mV, I set = 200 pA). (b) A typical tunnel-ing spectrum measured in a energy window far beyond thesuperconducting gap ( T = 1 . V set = 300 mV, and I set =500 pA). (c) Two tunneling spectra measured at the markedpositions by the red and black crosses in the lower-left inset in(a) ( T = 1 . V set = 10 mV, and I set = 200 pA). The spec-trum in red color is measured at the center of the red crossin the hollow, while the spectrum in black color is measuredat the center of black cross in the flat area. The blue dashedline shows the fitting curve by the Dynes model with a slightlyanisotropic s -wave gap function. (d) A spatially resolved tun-neling spectra measured along the yellow dashed line in thelower-left inset in (a) ( T = 0 . V set = 20 mV, and I set = 200 pA). The positions of the coherence peaks are markedby the green arrows. The spectrum with green color is mea-sured at the center of the green cross shown in the lower-leftinset in (a), which exhibits a peak at bias voltage of about -2mV (marked by a blue arrow), and it may be the impurityinduced state. (e) The statistics of peak energies in 845 tun-neling spectra measured at randomly selected points in thearea of (a) ( T = 1 . V set = 10 mV, and I set = 200 pA).The blue arrows indicate the existence of low-energy peaks atabout ± . Figure 2(c) shows two tunneling spectra measured attwo marked positions in the lower-left inset in Fig. 2(a),i.e., one is measured at a position in a hollow, and theother is measured at a position on the flat area far awayfrom the hollows. One can see that the two spectrashow almost the same feature, which suggests that hol- lows have very little influence on the superconductivity.A slight suppression of the intensity of coherence peakscan be observed on the spectrum measured in the hol-low compared to that measured in the flat area. Bothof the two spectra show a full gap feature with a pairof coherence peaks locating at energies of about ± s -wave gap to fit the spectrum measured in the flat area.The best fitting result is shown as the dashed curve inFig. 2(c), and it requires a slightly anisotropic s -wavegap for the best fitting. The obtained gap function reads∆( θ ) = 4 . .
93 + 0 .
07 cos 2 θ ) meV, and the scatteringrate Γ = 0 . max is closeto the energy value of coherence peaks, and it is also sim-ilar to gap values of hole pockets of α and β or the elec-tron pocket of δ from the ARPES measurements [14]. Wealso measured a set of tunneling spectra along a dashedline in the lower-left inset in Fig. 2(a), and the spectraare shown in Fig. 2(d). All the spectra are homogeneousexcept for a slight change of the coherence peak energy.On the spectrum in green color shown in Fig. 2(d), onecan see that there is a small peak at about 2 mV markedby a blue arrow. It should be noted that this spectrum isnot measured in the hollow, and there is no any uniquefeature on the topography. The peak is likely to be thebound state induce by an impurity underneath the sur-face, which will be discussed below in Subsection III C.We then conduct the tunneling spectrum measurementall over the area in Fig. 2(a), and do the statistics topeak energies on 845 measured spectra. The result isshown in Fig. 2(e). The coherence peaks are mostly lo-cated from 4.4 to 5.4 meV from the statistics. About 2%of spectra have low-energy peaks within the energy rangeof ± (2 . ± .
4) mV, they can appear either at the hollowpositions or in the flat area.
B. Results of quasiparticle interference
QPI measurements and the related analysis are veryuseful because they can tell the information of the Fermisurface [27], the gap anisotropy [28, 29], as well as thegap signs [30–34] in a superconductor. We also mea-sure the differential conductance mapping and show aQPI mapping at E = 10 meV in Fig. 3(b). Althoughthe hollows in the topography do not affect the super-conductivity too much, standing waves can be clearlyseen surrounding these hollows. When we do the Fouriertransformation to the QPI mapping, we can obtain theFourier-transformed (FT-) QPI pattern and show it inFig. 3(d). In K12442, a previous ARPES work [14] ob-serve three hole pockets ( α , β , and γ ) around the Γ pointand one tiny electron δ pocket around M point. Weplot a sketch map of Fermi surfaces in Fig. 3(c). Herethe intra band scattering should locate around the cen-ter point of the FT-QPI pattern shown in Fig. 3(d), andthe simulated scattering results between the hole and theelectron pockets are plotted as the four grey patterns in FIG. 3. (a) Topographic image ( V set = 30 mV, I set = 200pA) and (b) the corresponding normal-state QPI mapping at E = 10 meV ( V set = 30 mV, I set = 200 pA) measured in thesame area. (c) Schematic plot of Fermi surfaces derived froma previous ARPES work [14]. (d) The Fourier transformedpattern of the QPI mapping in (b). (e) Line profile plot ofthe intensity of the FT-QPI pattern along the black dashedline in (d), and the arrows indicate the position of scatteringvectors connecting Γ and M points. (f) The simulated scat-tering patterns between the hole and electron pockets plottedas grey patterns with center of √ π/a from the center ofthe FT-QPI pattern. Here the grey patterns are the selectedpatterns in the self-correlated image of (c). And the arrowrepresents the scattering vector connecting Γ and M points.Comparing (d) and (f), one can see that the scattering be-tween hole and electron pockets has not been detected fromour experimental data. All measurements are carried out at0.7 K. Fig. 3(f). However, these scattering patterns have notbeen observed in the experimental data shown in (d). Itis more clear in the line-cut intensity of the differentialconductance shown in Fig. 3(e). It is almost featurelessnear the points of q = ±√ π/a which connects Γ and Mpoints in momentum space. The absence of the charac-teristic scattering patterns between the hole and electronpockets may be explained by following two possible rea-sons. (a) A low density of states at the Fermi energy forthe small electron δ pockets; (b) The unsensitive tunnel-ing matrix element effect. A detailed discussion is givenin the Section IV. Since we have not observed the scattering between thehole and electron pockets, we try to get some informa-tion of the intra-band scattering from the QPI data in alarge area. Results of QPI mappings and correspondingFT-QPI patterns are shown in Fig. 4. At zero energy,almost no clear features can be observed in QPI patternin Fig. 4(b), which is consistent with the full gap featurefrom tunneling spectrum measurements. At E = ± . E = ± . ± . π/a . These values are close to the parameters of thehole-like α pocket as determined from ARPES measure-ments [14]. C. Impurity bound states
In order to investigate low-energy peaks at about ± . ± ± FIG. 4. (a) A large-scale topographic image measured on the surface of K12442 ( V set = 10 mV, I set = 200 pA). (b)-(j) TheQPI mapping measured in (a) at different energies with B = 0 T and T = 1 . V set = 10 mV, I set = 200 pA). Circles in (a)and (c) mark positions of impurities with the bound state energy at about ± . . π/a which is a very small value. (t) The energy dispersion ofintensity in FT-QPI patterns along the diagonal direction marked by a blue dashed line in (m). The energy dispersion featureseems to be hole-like. The dashed curve is a guide line of a parabola, and we can obtain the energy E b ≈ ± ter of a bright spot and under different magnetic fields.The amplitude of the impurity induced peak lowers downwith increase of the magnetic field. The inset of Fig. 6(c)shows the enlarged view of the impurity induced peakin negative-energy side, and the peak energy is almostunchanged under the magnetic field of 4 T. From a pre-vious report, the field-induced peak-shift slope is about0.06 meV/T for the impurity bound state induced bya magnetic Fe-vacancy impurity with the Land´e factor g = 2 [35]. Based on this slope, we can calculate theenergy shift is about 0.24 meV when the field changesfrom 0 to 4 T. However, the energy shift is negligible forthe impurity bound state in the K12442 sample, we canargue that the impurity may be non-magnetic or weak magnetic. In addition, the peak feature is similar to thebound state peak of the As vacancy [36], so impuritiesare likely to be non-magnetic As vacancies in the FeAslayer underneath. D. Tunneling spectra measured on another kind ofterminated surface
In the K12442 sample, we also observe other areaswith different topographic features, and one example isshown in Fig. 7(a). This kind of surface is rarely ob-served with a possibility of once in 8 times cleavage. Onthis surface the hollows are much smaller than the ones
FIG. 5. (a) Topographic image ( V set = 20 mV, I set = 200 pA)and (b) QPI mapping at E = 2 meV ( V set = 20 mV, I set =200 pA) measured in the same area. One can see three brightspots in (b). (c) A set of tunneling spectra ( V set = 20 mV, I set = 200 pA) measured along the arrowed line in (a) or (b)crossing centers of these two spots. The tunneling spectra inred are the ones measured in the area of the bright spot. Allmeasurements are carried out at 1.7 K. shown in Fig. 2(a). However, from the atomically re-solved surface shown in the inset in Fig. 7(a), the latticeconstant is also about 5.3 ˚A which is close to the valueobtained in Fig. 2(a). Figure 7(b) shows a tunnelingspectrum measured in a wide bias range. The spectrumhas the similar behavior comparing with the one shownin Fig. 2(b): both of them show the particle hole asym-metry. The quantitative difference of them is the consid-erable bias-voltage dependence of d I/ d V in the negativebias side of the spectrum shown in Fig. 7(b). This sug-gests slightly different band structures in these two kindsof surfaces. In the area of Fig. 7(a), we can detect spectrawith different gap energies, and four examples are shownin Figs. 7(c)-7(f). In the spectrum shown in Fig. 7(f), wecan also see low-energy peaks at about ± . ±
10 meV on some spectra. The humps ontunneling spectra may be the feature of a larger super-conducting gap, or may be the bosonic mode which hasbeen observed in many FeSCs [37–39]. Figure 7(h) showsthe energy statistic results of all the peak features basedon 900 spectra measured in the area of Fig. 7(a). Onecan see that the coherence peak feature are in the range
FIG. 6. Temperature dependent evolution of the tunnelingspectra measured (a) at the bright-spot center and (b) faraway from any impurities. Specifically, (a) and (b) are mea-sured at centers of the red and yellow crosses marked in theinset of (a), respectively. (c) Magnetic field evolution of thetunneling spectra measured at the impurity center. The insetshows the enlarged view of the bound state peak at about − V set = 20 mV, I set = 200 pA. of ± (4-8) meV with possible local maxima at about ± . ± .
4, and ± . ± . FIG. 7. (a) Topographic image of another kind of terminatedsurface ( V set = 1 V, I set = 20 pA). Hollows in this topogra-phy have a lower density and a smaller averaged size whencompared with ones in Fig. 2(a). The inset shows the atomi-cally resolved topography measured in the flat area far awayfrom hollows ( V set = 100 mV, I set = 200 pA). (b) A typicaltunneling spectrum measured to high energy ( V set = 100 mV, I set = 200 pA). (c-f) Tunneling spectra measured at markedpositions in (a) ( V set = 30 mV, I set = 200 pA). The charac-teristic peaks are marked by arrows. (g) The statistics of thepeak energies derived from 900 spectra which are measured atpoints with a matrix of 30 ×
30 uniformly distributed in thearea of (a) ( V set = 50 mV, I set = 500 pA). All measurementsare carried out at 1.7 K. shift from about ± ± IV. DISCUSSIONS
On the surfaces of KCa Fe As F single crystals, weobserve the √ × √ FIG. 8. (a) Topographic image with an exposed low-lying areaof the under layer ( V set =50 mV, I set = 100 pA). The insetshows the line profile of the surface height along the arrowedline, and the exposed low-lying layer is about 1 ˚A by averagelower than the top surface layer. (b) A set of tunneling spectrameasured along the dashed line in (a) ( V set = 50 mV, I set =200 pA). (c) Color mapping of the coherence peak energy inpositive bias side based on 900 tunneling spectra measured atpoints with a matrix of 30 ×
30 uniformly distributed on thearea of (a) ( V set = 50 mV, I set = 200 pA). All measurementsare carried out at 1.7 K. composed by alkali metal atoms [23–25]. The hollow pop-ulation and distribution may be different in the surfaceterminated by alkaline-earth metal atoms. In this pointof view, and considering the observed features, the com-monly obtained top surface may be reconstructed by Katoms, while the rarely achieved surface may be recon-structed by the Ca atoms in K12442 samples. The hol-lows are either K or Ca vacancies in the two cases, whichmay be due to easy losing of these atoms in the cleavingprocedure. The missing K/Ca atoms on the surface willadjust the band structure slightly, which is supported bythe different features beyond the gap on spectra shownin Figs. 2(b) and 7(b).We observe obvious fully gapped feature in most tun-neling spectra measured in K12442 single crystals, whichindicates the absence of nodes and is consistent withother measurements [14–16]. Most of the coherence peakslocate in the energy range from 4 to 8 meV, and these gapvalues seem to be comparable to those reported previ-ously [14, 16, 40]. Since the dominant contribution of theFT-QPI is consistent with the intrapocket scattering ofthe α pocket, the obtained superconducting gap values onthe easily achieved surface are likely to be assigned to thishole pocket. Therefor the superfluid may be mainly con-tributed by the hole-like Fermi surfaces near Γ point. Thesituation is similar to that in CaKFe As : several holeand electron pockets are observed near Γ and M pointsby the ARPES measurement [41], but only the scatteringbetween two hole pockets is observed in FT-QPI patternsfrom the STM measurement [42]. The hump feature atabout ± . ± α bandnear Γ. However, the determined Fermi energy of the α band is only about 24 ± E F ≫ ∆ can-not be satisfied in K12442. This strongly suggests thatthe superconducting physics in K12442 material shouldpossess by itself an unconventional feature.In FeSCs, the scenario of s ± pairing is based on thenesting between the hole and electron pockets with sim-ilar sizes in the weak coupling scenario. This pairingmanner was firstly inferred from the QPI measurementson Fe(Se,Te) by comparing the difference when the ap-plied magnetic field is zero and finite[30]. This was laterfurther strengthened by the impurity effect[43] and phaseresolved QPI analysis [44]. However, this pairing mecha-nism is challenged in K12442 because the electron pocketat M point is too small [14], so the nesting condition can-not be satisfied. In our measurements, we cannot evenobserve the scattering pattern between the hole pocketsand tiny electron pockets in the FT-QPI result. Thereare two possible reasons for this. The first one is thetunneling matrix element effect due to which we cannotdetect the electron δ pocket. In fact we can only detectthe intrapocket scattering of α pocket, and we cannoteven detect the scattering related to β and γ pockets.Hence, it is not strange that we have not detected thescattering based on the δ pocket. The other possible rea-son is the low density of states for the δ pocket. Howeverin any case, very different sizes of the hole and electron pockets challenge the nesting picture of s ± -pairing in theweak coupling scenario. From tunneling spectra obtainedin this work, if the impurity is non-magnetic in nature aswe argued, the impurity bound states at about ± . s ± pairing [45]. V. CONCLUSION
In conclusion, by using scanning tunneling microscope,we have investigated the superconducting gaps and pair-ing mechanism of KCa Fe As F single crystals. Mostspectra exhibit a full gap feature with the gap valuefrom 4 to 8 meV. On few spectra, some peaks can beobserved at about ± . α pocket near Γ point. Thedispersion derived from the FT-QPI indicates a smallFermi energy of about 24 meV for the band forming the α pocket. This indicates a strong deviation from the ba-sic requirement of the weak coupling BCS theory. Ourresults shed new light in helping to clarify the supercon-ducting mechanism in iron based superconductors. ACKNOWLEDGMENTS
We appreciate useful discussions with A. V. Bal-atsky and Z. Y. Wang. This work was supportedby National Key R&D Program of China (GrantsNo. 2016YFA0300401, No. 2018YFA0704200, No.2017YFA0303100, and No. 2017YFA0302900), Na-tional Natural Science Foundation of China (GrantsNo. 12061131001, No. 11974171, No. 11822411, No.11961160699, No. 11674406, and No. 11674372), andthe Strategic Priority Research Program (B) of Chi-nese Academy of Sciences (Grants No. XDB25000000,and No. XDB33000000). H. L. is grateful for the sup-port from Beijing Natural Science Foundation (Grant No.JQ19002) and the Youth Innovation Promotion Associa-tion of CAS (Grant No. 2016004). ∗ [email protected] † [email protected] [1] P. J. Hirschfeld, M. M. Korshunov, and I. I. Mazin, Rep.Prog. Phys. , 124508 (2011).[2] Z. C. Wang, C. Y. He, S. Q. Wu, Z. T. Tang, Y. Liu, A. Ablimit, C. M. Feng, and G. H. Cao, J. Am. Chem. Soc. , 7856(2016).[3] Z. C. Wang, C. Y. He, Z. T. Tang, S. Q. Wu, and G. H. Cao, Sci. 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