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Europhysics Letters

PREPRINT

Observation of the second harmonic in superconducting current-phase relation of Nb/Au/(001)YBa2Cu3 Ox heterojunctions
P. V. Komissinski (? ) 1;3 , E. Il'ichev 2 , G. A. Ovsyannikov 3 , S. A. Kovtonyuk 3 , M. Grajcar 4 , R. Hlubina 4 , Z. Ivanov 1 , Y. Tanaka 5 , N. Yoshida 5 and S. Kashiwaya 6 1 Department of Microelectronics and Nanoscience, Chalmers University of Technology and GÔ eborg University, S-412 96, GÔ eborg, Sweden ot ot 2 Institute for Physical High Technology, Dept. of Cryoelectronics, P.O. Box 100239, D-07702 Jena, Germany 3 Institute of Radio Engineering and Electronics, RAS, Moscow 101999, Russia 4 Department of Solid State Physics, Comenius University, MlynskÆ Dolina, SK-842 48 a Bratislava, Slovakia 5 Department of Applied Physics, Nagoya University, 464-8603, Nagoya, Japan 6 Electrotechnical Laboratory, Umezono, Tsukuba, Ibaraki, 305-8568, Japan
PACS. 74.50.+r { Proximity e?ects, weak links, tunneling phenomena, and Josephson e?ects. PACS. 74.40.Gk { Tunneling. PACS. 74.80.Fp { Point contacts; SN and SNS junctions.

Abstract. { The superconducting current-phase relation (CPR) of Nb/Au/(001)YBa2 Cu3 Ox hetero junctions prepared on epitaxial c-axis oriented YBa2 Cu3 Ox thin ?lms has been measured in a single-junction interferometer. For the ?rst time, the second harmonic of the CPR of such junctions has been observed. The appearance of the second harmonic and the relative sign of the ?rst and second harmonics of the CPR can be explained assuming, that the macroscopic pairing symmetry of our YBa2 Cu3 Ox thin ?lms is of the d + s type.

Introduction. It is now well established that the dominant component of the superconducting order parameter in the cuprates has d-wave symmetry (see [1] and references therein). Moreover, it has become clear that in orthorhombic materials such as YBa2 Cu3 Ox (YBCO), a ?nite component with s-wave symmetry is admixed to the dominant d-wave order parameter. The early in-plane phase sensitive experiments imply that the d-wave component remains coherent through the whole sample [1], while an elegant c-axis tunneling experiment shows directly that the s-wave order parameter component does change sign across the twin boundary [2]. The above picture of the YBCO pairing state is challenged by the experimental observation of a ?nite c-axis Josephson current between heavily twinned YBCO and a Pb counterelectrode [3]. Namely, the contribution of the s-wave part of the YBCO order parameter to
(? ) Corresponding author. E-mail adress: ?lipp@fy.chalmers.se c À EDP Sciences


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the Josephson coupling between a conventional superconductor (superconductor with a pure s-wave symmetry of the order parameter, for example Pb or Nb) and YBCO should average to zero for equal abundances of the two types of twins in YBCO. In other words, the macroscopic pairing symmetry of twinned YBCO samples should be a pure d-wave [4]. Tanaka has shown that a ?nite second order Josephson current obtains for a junction between the s-wave and c-axis oriented pure d-wave superconductors [5]. However, measurements of microwave induced steps at multiples of hf =2e on the I -V curves of Pb/Ag/YBCO tunnel junctions imply dominant ?rst order tunneling [6]. Therefore the ?nite c-axis Josephson current has to result from a nonvanishing admixture of the s-wave component to the macroscopic order parameter of YBCO [4]. Two alternatives of how this can take place in the junctions based on twinned YBCO have been discussed in the literature: (i) Sigrist et al. have suggested that the phase of the s-wave component in YBCO does not simply jump from 0 to Ì upon crossing the twin boundary, but rather changes in a smooth way, attaining the value of Ì=2 right at the twin boundary [7]. The twinned YBCO sample is thus assumed to exhibit a macroscopic d + is pairing symmetry. A related picture has been proposed by Haslinger and Joynt, who suggest a d + is surface state of YBCO [8]. (ii) A di?erence in the abundances of the two types of twins implies a d + s symmetry of the macroscopic pairing state [9]. Let us point out that also structural peculiarities of other type (such as a lamellar structure in a preferred direction) may lead to the d + s macroscopic pairing symmetry. In this paper we report the observation of a large second harmonic of the Josephson current in Nb/Au/(001)YBCO junctions. By comparing the relative signs of the ?rst and second harmonics of the Josephson current, we show that the macroscopic d + s pairing symmetry is realized in our YBCO samples. Our results might be relevant also in search for so called "quiet" qubits which can be realized making use of junctions with a dominant second harmonic of the Josephson current [10]. Another promising route to fabricate such junctions is via 45Á grain boundary Josephson junctions [11, 12]. Experimental. In realization of the Josephson junctions between conventional superconductors and c-axis oriented high-temperature ones an extensive use has been made of the Pb/Ag/(001)YBCO hetero junctions [3]. In search for a combination of the superconducting counterelectrode and a normal-metal bu?er layer with the highest possible interface quality, in the present work we have decided to study the Nb/Au/(001)YBCO hetero junction. Our epitaxial (001)-oriented YBCO ?lms with thicknesses of 150 nm were obtained by laser deposition on (100) LaAlO3 and (100) SrTiO3 substrates. The ?lms are usually twinned in the ab-plane. The superconducting transition temperature of our YBCO ?lms was determined by magnetic susceptibility measurements as Tc = 88 ? 90 K. The YBCO ?lms were in situ covered by a 8 ? 20 nm thick Au layer, thus preventing the degradation of the YBCO surface during processing. Afterwards, 200 nm thick Nb counterelectrodes were deposited by DC-magnetron sputtering. Photolithography and low energy ion milling techniques were used to fabricate the Nb/Au/YBCO junctions. The interface resistance per unit area RB = RN S (where RN is the normal state resistance and S is the junction area) was RB = 10Å5 ? 10Å6 ?cm2 . Details of the junction fabrication were reported elsewhere [13]. Surface quality of the YBCO ?lms is very important when current transport in the c-axis direction is investigated. High-resolution atomic force microscopy reveals a smooth surface consisting of approximately 100 nm long islands with vertical peak-to-valley distance of Ì 3nm (?g. 1). We can exclude that substantial ab-plane tunnel currents Àow between YBCO and Nb at the boundaries of these islands. In fact, theory predicts formation of midgap states at the surface of semi-in?nite CuO2 planes [14, 15]. Therefore zero bias conductance peaks should be expected in the I -V characteristics at temperatures larger than the critical temperature


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of Nb, if the contribution of ab-plane tunneling was nonnegligible. However, no such peaks have been observed for all fabricated Nb/Au/YBCO junctions. Moreover, from the size of the islands and from the vertical peak-to-valley distance we estimate that the area across which ab-plane tunneling might take place is less than 6% of the total junction area. Since the interface resistances per square are of the same order of magnitude [3] for both, the c-axis and ab-plane junctions, we conclude that ab-plane tunneling from YBCO, if present, is negligibly small. We have measured more than 20 single junctions with areas in the range from 10 ? 10 Ém2 to 100 ? 100 Ém2 . At small voltages the typical I -V curves can be described by the resistively shunted junction model with a small McCumber parameter [16]. Typical critical current densities were jc = 1 ? 12 A/cm2 and jc RB = 10 ? 90 ÉV. The di?erential resistance vs: voltage dependence Rd (V ) exhibits a gap-like structure at V Ì 1:2 mV at T = 4:2 K (see ?g. 2). This structure has a BCS-like temperature dependence and disappears at TcR Ì 9:1 K, therefore we ascribe it to the superconducting energy gap of Nb. The CPR measurements were performed using a single-junction interferometer con?guration in which a junction of interest is inserted into a superconducting loop with an inductance L Ì 80 pH. We measure the impedance of a parallel resonance circuit inductively coupled to the interferometer as a function of the external magnetic Àux ?e threading the interferometer. The dimensionless CPR f (') = Is (')=Ic (where Is (') is the Josephson current) can be extracted from the following equations: ' = 'e Å ?f ('); k2 Q? f 0 (') tan ? = ; 1+ ?f 0 (') (1) (2)

where 'e = 2Ì?e =?0 , ' is the phase di?erence across the Josephson junction, the prime denotes a derivative with respect to ', ? is the phase shift between the driving current and the tank voltage at the resonant frequency, ? = 2ÌLIc =?0 is a normalized critical current, Q is the quality factor of the parallel resonance circuit, k is the coupling coeÁcient between the RF SQUID and the tank coil, and ?0 is the Àux quantum. This method, being di?erential with respect to ', provides a high sensitivity of the CPR measurement. Moreover, Is (') is measurable even if the thermal energy exceeds the Josephson coupling energy. In fact, critical currents down to 50 nA were recently detected at T = 4:2 K [17]. For the junction SQ10, ? varied between 0.4 and 0.27 for temperatures in the range T = 1:7 ? 6:0 K. Since ? < 1, we can extract the CPR from the ?('e ) dependence for the complete phase range (see ?gs. 3 and 4). Fourier analysis of the experimentally obtained CPR shows substantial ?rst and second harmonics and negligibly small higher-order harmonics. Therefore we can write (3) Is (') = I1 sin ' + I2 sin 2' for all temperatures below the transition temperature of Nb. The sign of I2 is always opposite to that of I1 . In what follows we use the convention that I1 > 0 and therefore I2 < 0. The ratio jI2 =I1 j grows with decreasing temperature reaching jI2 =I1 j Ì 0:16 at T Ì 1:7 K, when I1 = 1:57 ÉA and I2 = Å0:25 ÉA (see inset to a ?g. 4). We point out that the main result of this paper, namely the large negative value I2 =I1 Ì Å0:16 observed at low temperatures, is not the result of an indirect data analysis, but it follows directly from the measured ?('e ) dependences. In fact, one ?nds readily that d2 tan ? k2 Q? f 000 = ; 2 d'e (1 + ?f 0 )4 (4)


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where all derivatives are taken at ' = 0 or 'e = 0. Thus, the existence of the local minima of ?('e ) at multiples of Ì dictates that f 000 > 0, or, making use of Eq. (3), I2 =I1 < Å1=8. Note that neither the conventional tunneling theory nor the I and II theories by Kulik and Omelyanchuk predict such local minima on the derivatives of CPR [16]. Discussion. Let us estimate the transparency of the barrier between YBCO and Nb from the normal-state resistance per unit area RB . According to the band-structure calculations (for a review, see [18]), the hole Fermi surface of YBCO is a slightly warped barrel with an approximately circular in-plane cross-section (to be called Fermi line) with radius kF . In what follows, we represent the electron wavevector k in cylindrical coordinates, k = (k; Å; kz ). We estimate the uncertainty of the in-plane momentum as Ák Ì 2Ì=l, where l is the characteristic size of the islands on the YBCO surface (?g.1). We evaluate RB making use of the Landauer formula and note that only tunneling from a shell around the Fermi line with width Ák is kinematically allowed. The barrier transparency D(Å ) depends on the details of the c-axis charge dynamics in YBCO, with maxima in those directions Å, in which the YBCO c-axis Fermi velocity w(Å ) is maximal. Since for Å = Ì=4 and symmetry equivalent directions w(Å) is minimal [19], we expect that there will be 8 maxima of D(Å) on the YBCO Fermi line where D(Å) Ì D, which are situated at Å = Å 0 and symmetry equivalent directions. The modulation of the function D(Å ) depends on the thickness of the barrier between YBCO and Nb [20]. We consider two limiting distributions of the barrier transparency D(Å) along the YBCO Fermi line: (a) a featureless D(Å) Ì D and (b) a strongly peaked D(Å ), roughly corresponding to thin and thick barriers, respectively [20]. In the thick barrier limit the angular size of the maxima of D(Å) can be estimated as ÁÅ Ì Ák=kF . With these assumptions we ?nd RÅ1 = B hDie A; ?0 (5)

where A measures the number of conduction channels and h:::i denotes an average over the junction area. In the thin and thick barrier limits, we ?nd A Ì kF Ák=Ì and A Ì 2Ák2 =Ì, A respectively. Taking l Ì 100 nm and kF Ì 0:6 ÊÅ1 [21], the measured RB = 6 ? 10Å5 cm2 of the junction SQ10 can be ?tted with hDithin Ì 1:7 ? 10Å5 and hDithick Ì 8:3 ? 10Å4 . Since we have observed no midgap surface states in the Rd (V ) curves, we can neglect the surface roughness, and the Josephson current can be calculated from [22] Is (') = X 2e X D?R ?k sin ' ; kB T h É 2R k + D [!2 + R k +?R ?k cos '] !
k;Å

(6)

where the sum over k; Å is taken over the same regions with areas A as in Eq. (5), ?R and p ?k are the Nb and YBCO gaps, respectively, and i = ! 2 +?2 with i = R; k. Keeping i only terms up to second order in the (small) junction transparency D, the Josephson current densities ji = Ii =S read j1 (T )R j2 (T )R where ?? = Ì ?d [2 d limits, respectively. ?d and ?s are the ?R and ?s . The
B

B

?s ?R (T ) ; ?? e d Å Æ ?R (T ) Ì hD2 i ?R (T ) tanh ÌÅ ; 8 hD i e 2kB T Ì

(7) (8)

ln(3:56?d =TcR )]Å1 In Eqs. (7,8) we d-wave and s-wave factor ?s =?? can d

and ?? = ?d j cos 2Å0 j in the thin and thick barrier d used the YBCO gap ?(Å) = ?s + ?d cos 2Å , where gaps. We have assumed that ?? is larger than both, d be estimated from the measured j1 RB products for


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Josephson junctions between untwinned YBCO single crystals and Pb counterelectrodes. For such junctions j1 (0)RB Ì 0:5 ? 1:6 meV [3]. Using the Pb gap ?R = 1:4 meV in Eq. (7), we obtain ?s =?? Ì 0:36 ? 1:1. d Note that within the above microscopic d + s scenario, the signs of I1 and I2 are di?erent. This feature remains valid also in the macroscopic d + s scenario, whereas within the macroscopic d + is picture, the same signs of I1 and I2 are expected. Thus we conclude that the ?nite ?rst harmonic has to be due to the macroscopic d + s symmetry of our YBCO sample. In fact, detailed structural studies show that for suÁciently thin YBCO ?lms, the abundances of the two types of twins can be di?erent even for ?lms grown on the cubic substrate SrTiO3 [23]. If we denote the twin fractions as (1 + Á )=2 and (1 Å Á )=2, then the measured ?rst harmonic of the CPR, hj1 i, is proportional to the deviation from equal population of twins, hj1 i = Áj1 [9]. Using ?R = 1:2 meV determined from the Rd (V ) data and our estimate ?s =?? Ì 0:36 ? 1:1, we ?nd that the measured ?rst harmonic hj1 i for the junction SQ10 can d be ?tted with Á Ì 0:07 ? 0:21, which is in qualitative agreement with [23], where Á Ì 0:14 for 1000 Ê thick YBCO ?lms has been observed. A Fitting the measured j2 RB of the junction SQ10 by Eq. (8) we obtain hD2 i=hDi Ì 3:2 ? 10Å2 , which is much larger than both hDithin and hDithick . This diference can be explained provided the junction transparency D is a Àuctuating function of the position r. In fact, adopting the WKB description of tunneling [20], we write D(s(r)) = exp(Ås0 Å s(r)), where s0 is the WKB tunneling exponent and s(r) its local deviation from the mean. Assuming a Gaussian distribution of s R h a mean deviation Ä, P (s) / exp(Ås2 =Ä 2 ), we estimate the wit s spatial averages as hDn i = Å0 0 dsP (s)Dn (s). In the thin barrier limit, the values hD2 ithin = s 8:6 ? 10Å7 and hDithin = 2:3 ? 10Å5 required to ?t the experiments correspond to an average WKB exponent sthin Ì 15:5 with Äthin Ì 4:3. In the thick barrier limit we obtain sthick Ì 9:1 0 0 and Äthick Ì 2:8. We would like to emphasize that, because of it's stochastic origin, the ratio I2 =I1 is hard to control experimentally. This explains why only 2 out of 7 measured samples exhibited a measurable second harmonic. Let us consider also the second harmonic generation by a mechanism proposed by Millis for planar junctions [24]. We can view the junction as a checkerboard of 0 and Ì junctions with a lattice constant a (characteristic size of an YBCO twin) and local critical current density j1 . As shown by Millis, spontaneous currents are generated in the ground state of such a junction and the junction energy is minimized for the phase di?erence ?Ì=2. An explicit calculation in the limit a; ÈR Ï È Ï Èc (where È; Èc are the ab-plane and c-axis penetration depths of YBCO and ÈR is the Nb penetration depth) yields j Comparing j2;
Millis 2;Millis

1 É j 2 aÈÈc ÌÅ p 0 1 : ?0 42

with Eq. (8), we ?nd p Å Æ2 8 2F ?s j2;Millis a ?R E0 ; Ì ? 2 j2 Ì ?d l É Èc É =È hc= hc

where E0 = e2 q0 =4ÌÂ0 with q0 = kF and 2Ák for a thin and thick barrier, respectively. F depends on the characteristic length scale L of the Àuctuations of the junction transparency: for L Ï a, F Ì hDi2 =hD2 i, whereas for L Ð a, F Ì 1. In order to estimate the upper bound of the ratio j2;Millis =j2 , we consider the thin barrier limit, take F Ì 1, ?s =?? Ì 1:1, d a Ì 10 nm, È Ì 240 nm, and Èc Ì 3 Ém (the last two values are valid for underdoped YBCO [25]) and we ?nd that j2;Millis =j2 < 0:03. Thus we can safely neglect the contribution of the Millis mechanism to the second harmonic of the CPR.


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Conclusion. We have observed the second harmonic I2 of the current-phase relation in caxis Nb/Au/YBCO hetero junctions. We have shown that the relative phases of the ?rst and second harmonics of the CPR together with their amplitudes I1 and I2 and the normal-state resistance of the Josephson junctions observed in the experiment can be explained making use of a single set of parameters within the standard microscopic d + s picture of the YBCO pairing state, assuming the di?erence in the abudances of the two types of twins and that the barrier Àuctuates along the junction. ??? We would like to thank P. Dmitriev for the Nb ?lms deposition, P. Mozhaev and K. I. Constantinyan for assistance in measurements, M. Yu. Kupriyanov, T. LÔ wander, V. Shumeiko, of A. Tzalenchuk, A. V. Zaitsev for fruitful discussions, and prof. T. Claeson for a critical reading of the manuscript. This work is supported by the INTAS program of the EU (Grant No. 97-1940), the DFG (Ho461/3-1), the Swedish Material Consortium of superconductivity, the Russian Foundation of Fundamental Research, and the Russian National Program on Modern Problems of Condensed Matter. Partial support by the D-wave Systems, Inc., by the NATO Science for Peace Program N97-3559, and by the Slovak Grant Agency VEGA (Grants No. 1/6178/99 and 2/7199/20) is gratefully acknowledged.
REFERENCES [1 [2 [3 [4 [5 [6 [7 [8 [9 [10 [11 [12 [13 [14 [15 [16 [17 [18 [19 [20 [21 [22 [23 [24 [25 ] ] ] ] ] ] ] ] ] ] ] ] ] ] ] ] ] ] ] ] ] ] ] ] ] Tsuei C. C. and Kirtley J. R., Rev. Mod. Phys., 72 (2000) 969. Kouznetsov K. A. et al., Phys. Rev. Lett., 79 (1997) 3050. Sun A. G. et al., Phys. Rev. B, 54 (1996) 6734. Walker M. B. and Luettmer-Strathmann J., Phys. Rev. B, 54 (1996) 588. Tanaka Y., Phys. Rev. Lett., 72 (1994) 3871. Kleiner R. et al., Phys. Rev. Lett., 76 (1996) 2161. Sigrist M. etal, Phys. Rev. B, 53 (1996) 2835. Haslinger R. and Joynt R., J. Phys.: Condens. Matter, 12 (2000) 8179. O0 Donovan C. et al., Phys. Rev. B, 55 (1997) 9088. Ioffe L. B. et al., Nature, 398 (1999) 679. Il'ichev E. et al., Phys. Rev. B, 60 (1999) 3096. Il'ichev E. et al., Phys. Rev. Lett., 86 (2001) 5369. Komissinskii F. V. et al., JETP, 89 (1999) 1160. Hu C., Phys. Rev. Lett., 72 (1994) 1526. Tanaka Y. and Kashiwaya S., Phys. Rev. Lett., 74 (1995) 3451. Likharev K. K., Rev. Mod. Phys., 51 (1979) 101. Ilichev E. et al., Rev. Sci. Instr., 72 (2001) 1882. Pickett W. E., Rev. Mod. Phys., 61 (1989) 433. Xiang T. and Wheatley J. M., Phys. Rev. Lett., 77 (1996) 4632. Wolf E. L., Principles of Electron Tunneling Spectroscopy (Oxford University Press, New York) 1985 Shen Z. X. and Dessau D., Physics Reports, 253 (1995) 1. Zaitsev A. V., Sov. Phys. JETP, 59 (1984) 1015. Didier N. et al., J. of Al loys and Compounds, 251 (1997) 322. Millis A. J., Phys. Rev. B, 49 (1994) 15408. Cooper S. L. and Gray K. E., in: Physical Properties of High Temperature Superconductors, Vol. IV (Ed. D. M. Ginsberg, World Scienti?c, Singapore) 1994.

Figure captions


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Fig. 1. Left panel: A high resolution AFM image of the surface of a 150 nm thick YBCO ?lm. Right panel: Height pro?le of the YBCO surface along the line indicated in the left panel. The peaks and valleys are shown by markers. The peak-to-valley distance is Ì3 nm and about 100 nm in the vertical and horisontal directions respectively. Fig.2(a) Typical I Å V curve and (b) di?erential resistance vs. voltage dependence Rd (V ) of a Nb/Au/YBCO junction with a 20 nm thick Au ?lm, measured at T = 4:2 K. The low voltage part of the I Å V curve ( V Ç 0:3 mV) is shown on the inset. Fig. 3. Phase shift ? as a function of 'e for the junction SQ10 at T =1.7, 2.5, 3.5, 4.2, and 6.0 K (from bottom to top). Fig. 4. The current-phase relation I (') of the junction SQ10 at T =1.7, 2.5, 3.5, 4.2, and 6.0 K (from top to bottom). Inset: Temperature dependence of I1 (squares) and jI2 j (circles). Solid lines are ?ts to Eqs. (7,8) using ?R (T ) = ?R (0) tanh[?R (T )TcR =?R (0)T ].


Fig. 1


0.5

20

10 8
-0 .3 0 .0 0 .3

I, ÅA

0

-2 0

I, mA

0.0

V, mV

(a)


6 4

Nb

2

(b)
-0.5 -2 -1

V, mV

0

1

2

0

Fig. 2

Rd, a.u.


1.0

,rad

0.5

0.0 -4 -3 -2 -1 0 1 2 3 4

e/

Fig. 3


1.5

I( ), Å A

1.0
1.5

|I 2 |, A Å 1,

0.5 0.0 0.0

1.0 0.5 0.0 1 2 3 45 T, K 6 7

0.2

0.4

/

0.6

0.8

1.0

Fig. 4.