Influence of the Fermi surface geometry on a Josephson effect between an iron-pnictide and conventional superconductors
A. A. Kalenyuk, E. A. Borodianskyi, A. A. Kordyuk, V. M. Krasnov
IInfluence of the Fermi surface geometry on a Josephson effect between aniron-pnictide and conventional superconductors
A. A. Kalenyuk , , E. A. Borodianskyi , A. A. Kordyuk , , and V. M. Krasnov , ∗ Department of Physics, Stockholm University, AlbaNova University Center, SE-10691 Stockholm, Sweden; Institute of Metal Physics of National Academy of Sciences of Ukraine, 03142 Kyiv, Ukraine; Kyiv Academic University, 03142 Kyiv, Ukraine; and Moscow Institute of Physics and Technology, State University, 141700 Dolgoprudny Russia.
We study Josephson junctions between a multi-band iron-pnictide Ba − x Na x Fe As and con-ventional s -wave superconductors Nb and Cu/Nb bilayer. We observe that junctions with a Cuinterlayer exhibit much larger I c R n , despite a weaker proximity-induced superconductivity. Thiscounterintuitive result is attributed to the difference in Fermi surface geometries of Nb and Cu,which leads to a selective one-band tunneling from Cu and a non-selective multi-band tunnelngfrom Nb. The latter leads to a mutual cancellation of supercurrents due to the sign-reversal s ± symmetry of the order parameter in the pnictide. Our results indicate that Fermi surface geome-tries play a crucial role for pnictide-based junctions. This provides a new tool for phase sensitivestudies and paves a way to a conscious engineering of such junctions. Electronic structure of superconductors is usually quitecomplicated, even for low- T c materials, such as the tran-sition metal Nb. Nevertheless, a simple description ofJosephson effects, which does not take into account com-plex Fermi surface (FS) geometry, works remarkably wellfor conventional superconductors [1, 2]. This happens be-cause probabilities of electron and Cooper-pair tunnelingare similar [3]. Together with a momentum-independent s -wave energy gap, ∆, it leads to the inverse relationshipbetween the normal resistance, R n , and the critical cur-rent, I c . Thus, the I c R n product becomes a universalfunction of ∆, independent of FS geometry [4].This universality, however, breaks for unconventionalmulti-band superconductors. A particularly drastic devi-ation should occurs in the case of sign-reversal order pa-rameter [5–8]. This occurs in cuprate and iron-based su-perconductors, which are believed to have d -wave [9, 10]and s ± [11–14] symmetries, respectively. In this case, I c depends on gap values in each band, and the I c R n isband-structure-sensitive and not universal [5–8, 15].In this work we fabricate and study high-qualityJosephson junctions (JJ’s) between single crystals of aniron-pnictide Ba − x Na x Fe As (BNFA) and conventionallow- T c superconductors made of either Nb film or Cu/Nbbilayer. Both types of JJ’s exhibit clean and clear Joseph-son phenomena. However, JJ’s with a Cu interlayer ex-hibit almost two order of magnitude larger I c R n , de-spite a weaker proximity-induced superconductivity inCu. This counterintuitive result is attributed to the dif-ference in FS geometries of Nb [multiple FS’s at variousparts of the Brillouin zone (BZ)] and Cu [a single quasi-spherical FS]. Therefore, tunneling from Nb takes placeinto all bands of BNFA. Due to the sign-reversal s ± orderparameter in BNFA, this leads to a mutual cancellationof supercurrents and a very small I c R n ∼ µ V. To thecontrary, tunneling from Cu occurs predominantly intoone sub-band avoiding such cancellation and leading toa significantly larger I c R n (cid:39) µ V. Our results indi- cate that FS geometries play a crucial role for JJ’s withmulti-band, sign-reversal superconductors. This providesa new tool for fundamental studies of unconventional su-perconductivity and opens a possibility for optimizationand adjustment of junction characteristics.Figure 1 (a) represents a scanning electron microscope(SEM) image of the BNFA-Cu/Nb sample. Our samplescontain six junctions made on a freshly cleaved BNFAsingle crystal. Fig. 1 (b) shows a closeup on the junc-tion. Here the vertical strip represents the window inSiO isolation layer and the horizontal strip - the topcontact electrode. Micrometer-size JJ’s are formed atthe overlap between the two strips. As the top electrodewe use either pure Nb film ( ∼
200 nm thick) or Cu(15nm)/Nb(180 nm) bilayer deposited by magnetron sput-tering in a single cycle without breaking vacuum. Detailsof sample fabrication, experimental setup and a list of JJparameters can be found in the Supplementary [15].Multiterminal configuration of our samples allows si-multaneous measurements of junction and crystal char-acteristics [23, 24]. The blue line in Fig. 1 (c) shows thein-plane resistive transition of BNFA. At T ∼
150 K thereis a kink in R ( T ), corresponding to a structural transi-tion and spin-density-wave (SDW) ordering [12, 14]. Thesuperconducting transition occurs at T c ( BN F A ) (cid:39) T c indicate that the BNFA crystal is moderatelyunderdoped. The red line in Fig. 1 (c) shows a simulta-neously measured resistive transition of a junction. Ithas two steps, first at T c ( BN F A ) and the second at T c ( N b ) ∼ I - V ) charac-teristics at different T for (d) BNFA-Nb and (e) BNFA-Cu/Nb JJ’s. In both cases the I - V ’s have the shape typ-ical for resistively shunted JJ’s [1, 2] with a well defined I c and R n . Green, blue and red curves are measured atzero field. The wine-color line in Fig. 1 (d) shows the I - V at T (cid:39) . a r X i v : . [ c ond - m a t . s up r- c on ] F e b J4 (x20)J2 R n ( m Ω ) T (K)(f) FIG. 1. (Color online). (a) and (b) SEM images of the BNFA-Cu/Nb sample. The sample contains six junctions J1-6 (a),formed at a cross-like overlap between a window in the insulation SiO layer and top electrodes (b). (c) Resistive transitions of ajunction (J2, red) and BNFA crystal (blue) for the BNFA-Cu/Nb sample. (d) and (e) I - V curves at different temperatures and H = 0 for junctions at (d) BNFA-Nb and (e) BNFA-Cu/Nb samples. The wine curve in (d) represents I - V at T (cid:39) . H (cid:107) = 15 mT. It demonstrates a complete suppression of I c by a modest in-plane magnetic field. (f) Temperature dependenciesof normal resistances for BNFA-Nb (red) and BNFA-Cu/Nb (blue) junctions. B (cid:107) = 15 mT. It is seen that I c is completely suppressedby a small parallel field, much smaller than the uppercritical fields of BNFA [23, 25] and Nb [26]. Therefore,in such a field we can carefully measure temperature de-pendence R n ( T ), as shown in Fig. 1 (f). The modest up-turn of R n with decreasing T is quite common for c -axischaracteristics of high- T c superconductors, commonly as-sociated with a pseudogap [27].Suppression of I c by small parallel field is causedby flux quantization in the junction. Figure 2 (a)shows I c ( H (cid:107) ) modulations at different temperatures fora BNFA-Cu/Nb JJ. Fig. 2 (b) represents normalized I c /I c (0) versus flux curves for BNFA-Nb (blue) andBNFA-Cu/Nb (red) JJ’s at low T . Both types of JJ’s ex-hibit clear Fraunhofer modulation depicted by the blackline. This is a figure of merit indicating good uniformityof JJ’s [1, 2].Figure 2 (c) shows I - V curves of a BNFA-Cu/Nb JJwithout (black) and with (red) applied high-frequencyelectromagnetic radiation at f (cid:39)
74 GHz at H = 0 and T (cid:39) . V = hf / e .Fig. 2 (d) shows the normalized differential conduc-tance for this I - V as a function of V /V . It reveals nu- merous subharmonic Shapiro steps. This indicates thestrongly non-sinusoidal current-phase relation in the JJ[28], which is indeed anticipated for s - s ± JJ’s [7, 8]. Onthe other hand, the non-sinusoidality may also be causedby the proximity effect in the Cu/Nb bilayer [29].Thus, our JJ’s exhibit clean and clear dc- and ac-Josephson effects. The high quality of the JJ’s togetherwith a good reproducibility of junction parameters (seethe Supplementary [15]) allows us to investigate genuinecharacteristics of composing them superconductors (asopposed to interface defects). Figs. 2 (e) and (f) showtemperature dependencies of (e) the critical current den-sity J c and (f) the I c R n product for both types of junc-tions. Despite similarities in behavior, the same BNFAcrystal [15] and fabrication procedure, the two types ofJJ’s exhibit largely (almost by two orders of magnitude)different I c R n values. BNFA-Nb JJ’s have a very small I c R n (cid:39) µ V [24], much smaller than ∆ /e > I c R n (cid:39) µ V. The difference can be clearly seen inthe I - V curves from Figs. 1 (d) and (e). The reportedremarkable influence of the thin Cu interlayer is the keyobservation of this work. (a) (e)(c)(d) (f)(b) I c R n ( µ V ) T / T c µ H ll (mT) I ( m A ) f = 77 GHz f = 77 GHz T = 0.4 KBNFA-Cu/Nb, J3 T = 0.4 K FIG. 2. (Color online). (a) Modulation of the critical current versus in-plane magnetic field for a BNFA-Cu/Nb junctionsat different temperatures. (b) Comparison of I c versus flux modulation patterns of BNFA-Cu/Nb (red), BNFA-Nb (blue)and Fraunhofer pattern (black). (c) I - V characteristics of BNFA-Cu/Nb junction with (red) and without (black) microwaveradiation. The primary Shapiro step is clearly seen. (d) Differential conductance versus inverse voltage, demonstrating presenceof sub-harmonic Shapiro steps. (e) Temperature dependencies of critical current densities of BNFA-Cu/Nb (blue, left scale)and BNFA-Nb (red, right scale) junctions. (f) Temperature dependencies of I c R n products for the same junctions. Notea big difference of I c R n values. The dotted black line represents a normalized theoretical curve for conventional s -wavesuperconductors [4]. The dashed black line shows a simulated dependence for an s - s ± junctions from Ref. [8]. The increase of I c R n in BNFA-Cu/Nb JJ’s is associ-ated with the increase of R n . The latter indicates thatthe interface transparency, β , between BNFA and Cuis reduced compared to BNFA-Nb. Yet, as mentionedabove, this does not explain the increase of I c R n becauseusually I c ∝ /R n and I c R n is independent of β .The proximity induced superconducting order pa-rameter in Cu at the junction interface is Φ N (cid:39) β Ψ S exp( d N /ξ N ), where Ψ S is the order parameter inNb, d N = 15 nm is the Cu layer thickness and ξ N isthe coherence length in Cu. According to Ref. [30],for thin sputtered Cu films ξ N (cid:39) (cid:112) T c ( N b ) /T (nm),where T c ( N b ) (cid:39) ξ N (0 . K ) (cid:39)
100 nm, ξ N (3 K ) (cid:39)
30 nm and ξ N ( T c ( N b )) (cid:39)
18 nm. Thus, ourCu interlayer is always thinner than ξ N . Although Cuand Nb films are deposited without breaking vacuum,the Cu/Nb interface transparency is modest, β (cid:39) . s -wave superconductors, theproximity effect leads to the reduction of I c R n [31]. Thisis opposite to our observation. This discrepancy pointsout that the unconventional (non- s -wave) symmetry ofthe order parameter in BNFA plays an essential role. Inparticular, the extremely small I c R n of BNFA-Nb junc-tions provides evidence for the sign-reversal s ± symmetryin BNFA, due to which supercurrents from bands withopposite signs of ∆ cancel each other [24].For a more quantitative understanding we consider FSgeometries of involved metals. Figures 3 (a-c) show DFTcalculated three-dimensional images of Fermi surfaces forCu (a), Nb (b) [32, 33] and BNFA (c) [34]. FS of Cuis simple quasi-spherical. The transition metal Nb has avery complex FS with many small pockets spread over theBZ. BNFA has two bunches of the FS sheets, the threelarge quasi-cylinders in the center and the propeller-likeFS’s at the corners of the BZ [35, 36]. Those bunches arebelieved to have opposite signs of ∆ [12, 13].Electron tunneling between two metals usually con- (a) (b) (c)(d)(e) (f)(g) (h)(i) k y ( π / b ) k y ( π / b ) -1.0 -0.5 0.0 0.5 1.0-1.0 -0.5 0.0 0.5 1.0 k x (2 π / a ) k x (2 π / a ) k y ( / Å ) k y ( / Å ) ‹ k x › (1/Å) k x (1/Å) k x (1/Å) Cu Nb BNFA ‹ k x › (1/Å) ‹ k y › ( / Å ) ‹ k y › ( / Å ) BNFA - CuBNFA - NbCuCuNbNb CuCuNbNb
0 0.5 1
FIG. 3. (Color online). (a-c) The Fermi surface topologies in the 1st Brillouin zone for (a) Cu, (b) Nb and (c) BNFA. (d)and (e) The k z -integrated projections of Fermi surfaces on the (001) plane for Cu (d) and Nb (e). (f) and (g) The sameprojections averages over the in-plane momentum angle, representing the effective ( k z -integrated) density-of-states distributionfor poly-crystalline Cu (f) and Nb (g) films. (h) and (i) Product of k z -integrated Fermi surfaceprojection of BNFAwith effectivedensity-of-states for Cu (h) and Nb (i). It can be seen that for BNFA-Cu junctions tunneling current flows predominantly intothe propeller-like corner bands of BNFA (h). On the other hand, for BNFA-Nb junctions the tunneling current is distributedrelatively uniformly between central and corner bands. serves the in-plain momentum k (cid:107) = ( k x , k y ). Therefore,the total single- electron current can be written as J ∝ (cid:73) T A ( k z , k (cid:107) ) A ( k z , k (cid:107) )( f − f ) d k (cid:107) dk z dk z , where T is the tunneling matrix element between initialand final states, ( k z , k x , k y ) and ( k z , k x , k y ), in the twoelectrodes, A , are the spectral functions (momentum-dependent density of states) and f , are the corre-sponding distribution functions. The key band-structure- dependent factor is the density of states projection on thejunction plane, which can be integrated independently N i ( k (cid:107) ) = (cid:90) A i ( k zi , k (cid:107) ) dk zi , ( i = 1 , . (1)Figs. 3 (d) and (e) show such projections for Cu and Nb.The corresponding projection for BNFA is pretty similarto the pattern, shown in Fig. 3 (i).For comparison with experiment we must take into ac-count the polycrystalline structure of Cu and Nb elec-trodes and make an average with respect to random crys-talline orientation. This is similar to averaging with re-spect to rotation of k x,y axes. Figs 3 (f) and (g) showthus averaged projections, < N i ( k x , k y ) > , for polycrys-talline Cu and Nb. The key difference is that due to thequasi-spherical FS of Cu, the polycrystalline density ofstates projection keeps the circular shape with the radiusgiven by the Fermi momentum. To the contrary, aver-aging for multi-band polycrystalline Nb leads to a moreuniform distribution of the density of states.Figs. 3 (h) and (i) show a product of the density ofstate projections (h) < N Cu ( k x , k y ) > N BNF A ( k x , k y ) forBNFA-Cu/Nb and (i) < N Nb ( k x , k y ) > N BNF A ( k x , k y )for BNFA-Nb junctions. It gives a hint about contribu-tion of the two BNFA bands in electrical current throughthe junction. For BNFA-Nb JJ’s both BNFA bands par-ticipate approximately equally due to fairly uniform dis-tribution of < N Nb ( k x , k y ) > in the BZ projection, Fig.3 (g). To the contrary, the highly non-uniform, circular-shape < N Cu ( k x , k y ) > , Fig. 3 (f), blocks tunneling intothe central band of BNFA.For calculation of supercurrent, A i should be replacedby A i Ψ i , where Ψ i is the superconducting order param-eter in the corresponding metal. For Nb and Cu/Nbwith s -wave order parameter Ψ is just a number. How-ever, for the unconventional two-band superconductorBNFA, which likely has the s ± symmetry, Ψ changessign between central and corner bands. For BNFA-NbJJ’s with similar transport contribution of the two bandsthis leads to an almost complete cancellation of the totalsupercurrent [24]. However, for BNFA-Cu/Nb JJ’s thecancellation is much smaller because tunneling from cen-tral bands is suppressed. Therefore, such analysis qual-itatively explains larger values of both R n and I c R n inBNFA-Cu/Nb junctions.To conclude, we fabricated and studied high-qualityJosephson junctions between an iron-pnictide supercon-ductor Ba − x Na x Fe As and either a conventional low- T c superconductors Nb or a Cu/Nb bilayer. Remarkably,we observed that addition of a very thin (15 nm) Cu in-terlayer changes drastically junction properties and, inparticular, increases the I c R n product by almost two or-ders of magnitude. The latter is opposite to expectationsfor proximity-coupled junctions made of conventional s -wave superconductors [31]. This counterintuitive resultadds to evidence for the unconventional s ± symmetry ofthe order parameter in the pnictide. The phenomenonis explained qualitatively taking into account particu-lar Fermi surface geometries of involved metals. It isshown that the multi-band structure of Nb leads to sim-ilar contributions of both pnictide bands into electrontransport, which due to the sign-reversal s ± supercon-ducting order parameter in the two electronic bands ofthe pnictide, leads to the cancellation of the total super-current and results in a very small I c R n (cid:39) µ V [24].To the contrary, the simple quasi-spherical Fermi sur- face of Cu supports tunneling predominantly from onlyone band, avoiding the supercurrent cancellation and re-sulting in much larger I c R n (cid:39) µ V. Our results in-dicate that unlike for junctions made of conventional s -wave superconductors, for junctions with unconventionalsign-reversal superconductors the Fermi surface geometryplays a crucial role. This provides a new tool for phasesensitive studies of such materials and could probably ex-plain some of reported variations of I c R n values in pnic-tide JJ’s [8, 24, 37]. The reported material-dependence oftunneling into pnictide superconductors can be used foroptimization and conscious engineering of pnictide-basedJosephson junctions.The work was supported by the National ResearchFoundation of Ukraine (project 2020.02/0408) and theRussian Science Foundation (Grant No. 19-19-00594).The paper was accomplished during a sabbatical periodof V.M.K. at MIPT. We are grateful to A.N. Yaresko forproviding the results of DTF calculations, V.V. Zabolot-nyy for help with FS visualization, S. Aswartham,S. Wurmehl and B. B¨uchner for providing BNFA crys-tals. ∗ [email protected][1] A. Barone and C. Paterno, Physics and Applications ofthe Josephson Effect (Wiley, New York, 1982).[2] K. K. Likharev, Dynamics of Josephson Junctions andCircuits (Gordon and Breach Sc. Publ., Amsterdam,1986).[3] D.G. McDonald, The Nobel laureate versus the graduatestudent,
Physics Today , 46 (2001).[4] V. Ambegaokar and A. Baratoff, Tunneling between su-perconductors, Phys. Rev. Lett. , 486 (1963); ibid. ,104 (1963).[5] Y. Tanaka and S. Kashiwaya, Theory of Josephson effectsin anisotropic superconductors, Phys. Rev. B , 892(1997).[6] Y. Ota, M. Machida, T. Koyama, and H. Mat-sumoto. Theory of Heterotic Superconductor-Insulator-Superconductor Josephson Junctions between Single-and Multiple-Gap Superconductors, Phys. Rev. Lett. , 237003 (2009).[7] I. B. Sperstad, J. Linder, and A. Sudbø, Quantum trans-port in ballistic s ± -wave superconductors with interbandcoupling: Conductance spectra, crossed Andreev reflec-tion, and Josephson current, Phys. Rev. B , 144507(2009).[8] A. V. Burmistrova, I. A. Devyatov, A. A. Golubov, K.Yada, Y. Tanaka, M. Tortello, R. S. Gonnelli, V. A.Stepanov, X. Ding, H. H. Wen, and L. H. Green. Joseph-son current in Fe-based superconducting junctions: The-ory and experiment, Phys. Rev. B , 214501 (2015).[9] D. A. Wollman, D. J. Van Harlingen, W. C. Lee, D. M.Ginsberg, and A. J. Leggett, Experimental determinationof the superconducting pairing state in YBCO from thephase coherence of YBCO-Pb dc SQUIDs, Phys. Rev.Lett. , 2134 (1993). [10] C. C. Tsuei and J. R. Kirtley, Pairing symmetry incuprate superconductors, Rev. Mod. Phys. , 969(2000).[11] T.K. Ng and N. Nagaosa. Broken time-reversal symmetryin Josephson junction involving two-band superconduc-tors, EPL , 17003 (2009).[12] P. J. Hirschfeld, M. M. Korshunov, and I. I. Mazin, Gapsymmetry and structure of Fe-based superconductors, Rep. Prog. Phys. , 124508 (2011).[13] F. Wang, D.-H. Lee, The electron-pairing mechanism ofiron-based superconductors. Science , 200 (2011).[14] A. Chubukov, Pairing Mechanism in Fe-Based Supercon-ductors,
An. Rev. Cond. Matt. Phys. , 57 (2012).[15] See EPAPS Document No.XXX. The supplementary ma-terial provides additional information about (i) Sam-ple fabrication, (ii) Additional transport characterization(iii) Junction parameters, and (iv) Numerical analysis oftemperature dependence of I c R n in junctions between aconventional s -wave superconductor and a two-band s ± superconductor, and includes Refs. [16–22].[16] V. M. Krasnov, H. Motzkau, T. Golod, A. Rydh, S. O.Katterwe, and A. B. Kulakov, Comparative analysis oftunneling magnetoresistance in low- T c Nb/Al-AlOx/Nband high- T c Bi − y Pb y Sr CaCu O δ intrinsic Josephsonjunctions, Phys. Rev. B , 054516 (2011).[17] D. V. Evtushinsky, V. B. Zabolotnyy, L. Harnagea, A. N.Yaresko, S. Thirupathaiah, A. A. Kordyuk, J. Maletz,S. Aswartham, S. Wurmehl, E. Rienks, R. Follath, B.B¨uchner, and S. V. Borisenko, Electronic band structureand momentum dependence of the superconducting gapin Ca − x Na x Fe As from angle-resolved photoemissionspectroscopy, Phys. Rev. B , 094501 (2013).[18] P. Szab´o, Z. Pribulov´a, G. Prist´a˘s, S. L. Bud´ko,P. C. Canfield, and P. Samuely, Evidence for two-gap superconductivity in Ba . K . Fe As from di-rectional point-contact Andreev-reflection spectroscopy, Phys. Rev. B , 012503 (2009).[19] D Daghero, M Tortello, G A Ummarino and R SGonnelli, Directional point-contact Andreev-reflectionspectroscopy of Fe-based superconductors: Fermi surfacetopology, gap symmetry, and electron-boson interaction, Rep. Prog. Phys. , 124509 (2011).[20] Yu. G. Naidyuk, O. E. Kvitnitskaya, S. Aswartham, G.Fuchs, K. Nenkov, and S. Wurmehl, Exploring point-contact spectra of Ba − x Na x Fe As in the normal andsuperconducting states, Phys. Rev. B , 104512 (2014).[21] S. Ziemak, K. Kirshenbaum, S. R. Saha, R. Hu, J.-Ph. Reid, R. Gordon, L. Taillefer, D. Evtushinsky, S.Thirupathaiah, B. B¨uchner, S. V. Borisenko, A. Ignatov,D. Kolchmeyer, G. Blumberg and J. Paglione, Isotropicmulti-gap superconductivity in BaFe . . fromthermal transport and spectroscopic measurements, Su-percond. Sci. Technol. , 014004 (2015).[22] Y. F. Wu, A. B. Yu, L. B. Lei, C. Zhang, T. Wang, Y.H. Ma, Z. Huang, L. X. Chen, Y. S. Liu, C. M. Schnei-der, G. Mu, H. Xiao, and T. Hu, Superconducting NbNand CaFe . Co . AsF studied by point-contact spec-troscopy with a nanoparticle Au array,
Phys. Rev. B ,174502 (2020).[23] A. A. Kalenyuk, A. Pagliero, E. A. Borodianskyi, S. Aswartham, S. Wurmehl, B. B¨uchner, D. A. Chareev,A. A. Kordyuk, and V. M. Krasnov, Unusual two-dimensional behavior of iron-based superconductors withlow anisotropy,
Phys. Rev. B , 134512 (2017).[24] A. A. Kalenyuk, A. Pagliero, E. A. Borodianskyi, A.A. Kordyuk, and V. M. Krasnov, Phase-Sensitive Ev-idence for the Sign-Reversal s ± Symmetry of the Or-der Parameter in an Iron-Pnictide Superconductor UsingNb/Ba − x Na x Fe As Josephson Junctions,
Phys. Rev.Lett. , 067001 (2018).[25] Y. Liu, M. A. Tanatar, W. E. Straszheim, B. Jensen, K.W. Dennis, R. W. McCallum, V. G. Kogan, R. Prozorov,and T. A. Lograsso, Comprehensive scenario for single-crystal growth and doping dependence of resistivityand anisotropic upper critical fields in (Ba − x K x )Fe As (0 . (cid:54) x (cid:54) Phys. Rev. B , 134504 (2014).[26] A. Zeinali, T. Golod, and V. M. Krasnov, Surface su-perconductivity as the primary cause of broadening ofsuperconducting transition in Nb films at high magneticfields, Phys. Rev. B , 214506 (2016).[27] S. O. Katterwe, A. Rydh, and V. M. Krasnov, Doping-Induced Change in the Interlayer Transport Mechanismof Bi Sr CaCu O δ near the Superconducting Transi-tion Temperature, Phys. Rev. Lett. , 087003 (2008).[28] A. A. Golubov, M. Yu. Kupriyanov, and E. Il’ichev, Thecurrent-phase relation in Josephson junctions, Review ofModern Physics , 411-469 (2004).[29] V. M. Krasnov, N. F. Pedersen, V. A. Oboznov, and V.V. Ryazanov, Josephson properties of Nb/Cu multilay-ers, Phys. Rev. B , 12969 (1994).[30] V.M. Krasnov, V.A. Oboznov and V.V. Ryazanov,Anomalous temperature dependence of H ⊥ c in super-conducting Nb/Cu multilayer, Physica C , 335-339(1992).[31] A. A. Golubov, E.P. Houwman, J. G. Gijsbertsen, V.M. Krasnov, J. Flokstra, and H. Rogalla, Proximity ef-fect in superconductor-insulator-superconductor Joseph-son tunnel junctions: Theory and experiment,
Phys. Rev.B Bulletin of The American PhysicalSociety , L36.042 (2000).[34] A.N. Yaresko. Privat communication.[35] V. B. Zabolotnyy, D. S. Inosov, D. V. Evtushinsky, A.Koitzsch, A. A. Kordyuk, G. L. Sun, J. T. Park, D. Haug,V. Hinkov, A. V. Boris, C. T. Lin, M. Knupfer, A. N.Yaresko, B.B¨uchner, A. Varykhalov, R. Follath, and S.V. Borisenko, ( π, π ) electronic order in iron arsenide su-perconductors, Nature , 569 (2009).[36] A. A. Kordyuk, V. B. Zabolotnyy, D. V. Evtushinsky, A.N. Yaresko, B. B¨uchner, S. V. Borisenko. Electronic bandstructure of ferro-pnictide superconductors from ARPESexperiment.
J. Supercond. Nov. Magn. , 2837 (2013).[37] S. Schmidt, S. D¨oring, N. Hasan, F. Schmidl, V. Tym-pel, F. Kurth, K. Iida, H. Ikuta, T. Wolf, and P. Seidel,Josephson effects at iron pnictide superconductors: Ap-proaching phase-sensitive experiments, Phys. Stat. Sol.B254