387481a0Nature3876632199705294814830028-0836199710.1038/387481a01476-467919977 April 199729 May 1997ukNatureNatureNATUREnatureNature is a weekly international journal publishing the finest peer-reviewed research in all fields of science and technology on the basis of its originality, importance, interdisciplinary interest, timeliness, accessibility, elegance and surprising conclusions. Nature also provides rapid, authoritative, insightful and arresting news and interpretation of topical and coming trends affecting science, scientists and the wider public./nature/journal/v387/n6632issueJournal homeArchiveCurrent issueAdvance online publicationPrivacy policySubscribeNature Publishing GroupSupplementsCurrent issue387481a0Pure dx2 - y2 order-parameter symmetry in the tetragonal superconductor TI2Ba2CuO6+[delta]
AU  - Tsuei, C. C.
AU  - Kirtley , J. R.
AU  - Ren, Z. F.
AU  - Wang, J. H.
AU  - Raffy, H.
AU  - Li, Z. Z.[ast] IBM T.J. Watson Research Center, PO Box 218, Yorktown Heights, New York 10598, USA[dagger] Superconducting Materials Laboratory, Department of Chemistry and New York State Institute on Superconductivity, State University of New York, Buffalo, New York 14260, USA[Dagger] Laboratoire de Physique des Solides, Universite Paris-sud, 91405 Orsay, FranceCrucial to the successful development of a theoretical model for high-temperature superconductivity is knowledge of the symmetry of the order parameter (or wavefunction) that describes the pairing of electrons in the superconducting state. Several experimental studies1-8 provide convincing evidence for an anisotropic order parameter, consistent







with a dx2- y2 symmetry. But none of these earlier experiments could rule out unambiguously an additional contribution from isotropic s-wave pairing; these experiments either involved superconductors with an orthorhombic crystal structure (for which a mixed s + d state is becoming increasingly







recognized as a likely consequence9,10), or their interpretation required detailed modelling of the uncertain effects of disorder and defects. Here we report the results of an experiment designed to circumvent these difficulties: the material studied is the single-layer tetragonal superconductor Tl2Ba2CuO6+[delta], and







the experimental configuration is such that the interpretation of the results relies solely on symmetry considerations. Our results indicate that this material has pure d dx2- y2 pairing symmetry, so providing a starting point for understanding the more complex mixed s + d state that appears to characterize







other high-temperature superconductors.An s + d pair state in orthorhombic copper oxides such as YBa2Cu3O7_5 (YBCO) is characterized by a gap function A(k) that transforms like s(tfx + fy + d(tfx - *[pound]), where hx and ky are components of the wavevector k, and s and d are measures of the amounts of s-wave and d-wave pairing in the admixture. Node lines in the gap function (A = 0) given by ky =







[plusmn] [(d + s)/(d - s)]l/2kx exist provided that d/s 1. The deviation of the slope of the node lines from the diagonals kx= [plusmn] ky of the Brillouin zone depends on the extent of the s + d admixture. Because the Pb-YBCO corner superconducting quantum interference device, SQUID, (or single Josephson junction) interference experiments rely on a sign change







between the a and b faces of YBCO, they cannot distinguish pure d-wave from mixed s + dpair states as long as d/s  1, The tricrystal experiments with YBCO and Tl2Ba2CuO6+6 (T12001) can, in principle, locate the nodes on the Fermi surface. However, this requires a systematic series of tricrystal experiments and a detailed model describing pair tunnelling beyond the







Sigrist-Rice formula11, which does not take into account interface roughness or disorder. Figure 1 Schematic diagram illustrating the geometrical configuration of a tetracrystal (100) SrTiO3 substrate, which effectively consists of two crystals rotated about the normal to the substrate plane by v/4 with respect to each other. For a given total misorientation angle 0 =







0, + 02, the pairtunnelling current is maximized9 for a symmetric grain boundary 0, = 62 = TT/S. We chose the angle a = 8, between the vertical ([010] in grain 1) and the grain boundaries (OA and OB) as 25[deg]. Also shown are the polar plots of the assumed dx2__y2 gap functions aligned with the crystallographic axes in the substrate. In the face of these difficulties,







it is important to demonstrate unambiguously the existence of a pure dx2_yi wave high- Tc copper oxide superconductor. Such an experiment would be significant in view of the substantial amount of theoretical work12"15 on the effect of s + d wave pairing on the properties of copper oxide superconductors, including the origin of high-temperature superconductivity. The







demonstration of a pure d-wave superconductor would help us to understand whether the coexistence of d and s singlet pairing channels is essential or just accidental to high- Tc superconductivity. It would also serve as a well defined starting point for understanding the more complex (d + s)-wave superconductors. Here we use a single-layer tetragonal T12201 film







deposited on a (100) SrTiO3 (STO) substrate (manufactured by Shinkosha Co., Tokyo) with a bicrystal geometry proposed by Walker and Luettmer-Strathmann9 (Fig. 1). The interpretation of this phase-sensitive test of pairing symmetry in this geometry depends only on symmetry considerations. We achieved the desired bicrystal wedge configuration by effectively fusing two







bicrystals along the dividing line MOM' in Fig. 1. There is a very important built-in reflection symmetry with respect to this line. The pair tunnelling current Is across a tunnel barrier between superconductors 1 and 2 is given by: where Y and Y2 are the pair wavefunctions in superconductors 1 and 2 respectively, and HT is the standard generic second-order tunnelling







hamiltonian16'17. Assuming that HT is invariant under reflection about the line MOM' (Fig. 1), for d-y2 [deg]r 4r pairing states a reflection symmetry operation ra on Is results in pair tunnelling across the gain boundary OA that is related to that along OB by: Figure 2 X-ray 0 scans (0[deg]-360[deg]) of the (105) reflection from the c-axis oriented epitaxial TI2201







film (a), and the (111) reflection of the same film's underlying SrTi03 substrate (b). Each consists of two sets (labelled with a closed triangle and an open circle) of four 90[deg]-apart peaks. In each case, there is a 45[deg] offset between the two sets of />-scan peaks, confirming the 45[deg]-rotated wedge bicrystal configuration. The angular difference projected







onto the basal plane between the (105) and (111) planes leads to the 45[deg] shift in [pound] between the corresponding peaks in a and b. Furthermore, there is a 1[deg] splitting in each of the peaks. The same conclusion may be reached by using the general expression for the Josephson current9. This sign change between the supercurrents across OA and OB means that any







superconducting loop enclosing the wedge tip O will result in a net IT phase, which produces a spontaneously generated half flux quantum. Figure 3 A three-dimensional presentation of the SSM image of the Josephson vortex trapped atthe wedge tip in a TI2201 blanketfilm deposited on a tetracrystal (100) SrTi03 substrate of the geometry shown in Fig. 1. The sample was







cooled in a field of 1 mG and imaged at 4.2 K. Figure 4 Modelling of the SSM imaging data in Fig. 3 for cross-sections along the directions OA (curve a) OB (curve b), and also through the peak of an isolated bulk single flux quantum in the same TI2201 film (curve c). The solid lines are fits to the data. The height of the pickup loop was determined to be 5.15 m by







fitting the bulk vortex data. If we assume that the total flux is h/Ae, the best fit to the data (solid curves in a and b) was obtained for a Josephson penetration depth of 12.5jjLm. If we allow both the total flux and the Josephson penetration depth to vary, we find PI PQ = 0.54 [plusmn] 0.04 and \ = 13.8 [plusmn] 1.5|xm, using a criterion of a doubling of the







best-fit x2 value. The solid line in curve b is derived from that in curve a by mirror reflection about they-axis. Curves b and c are offset by 0.05 and 0.1 units, respectively, for clarity. The oxygen-optimized 200-nm-thick c-axis oriented T12201 film (Tc = 83 K) was prepared by radio-frequency magnetron sputtering followed by a two-step post-annealing, first in air







to promote epitaxial film growth, and second in argon to optimize the compositional stoichiometry18. A standard X-ray diffraction (XRD) measurement on our T12201 film shows only (OO/) reflection peaks (/up to 30 have been observed) indicating that the sample is phase-pure and has strong epitaxy. The co-scan of the STO(200) reflection results in a double-peak rocking







curve. Each peak has a full-width at half-maximum of -0.035[deg] with a splitting of ˜0.1[deg], suggesting that the precision in the c-axis alignment of the grains in the STO substrate is -0.1[deg]. The rocking curve of the (0010) reflection of the T12201 film has a full-width at half-maximum of 0.35[deg], indicating high-quality c-axis epitaxial film growth. 0-scan







XRD measurements were made to assess the degree of in-plane alignment by monitoring the (105) reflection of the T12201 film and the (111) reflection of the STO substrate (Fig. 2). All of these XRD data indicate that both the substrate and the film are made of two parts, rotated with respect to each other about the c-axis by 45[deg], as intended. The 0-scan data also







suggests that there is an ˜1[deg] misorientation in each grain at the boundary line MOM' (Fig. 1). We show below that this has no effect on the pairing symmetry test. For a definitive conclusion of the present pairing symmetry test, it is essential to establish that the crystal structure of the T12201 films used here is tetragonal. However, it is impossible to







distinguish between the tetragonal and orthorhombic structures by XRD data alone. The XRD signatures of orthorhombicity, such as the splitting of (110) tetragonal reflections into (020) and (200) peaks, are not observable in the c-axis oriented films, which are characterized only by the (00/) reflections. The tetragonality of our T12201 epitaxial films was previously







demonstrated by the combined use of indirect evidence from Raman spectroscopy and XRD18. More recently, the tetragonal crystal structure and the absence of twinning in these films have been well established by bright field imaging transmission electron microscopy, selected area electron diffraction, and convergent beam electron diffraction19. We used a scanning SQUID







microscopy (SSM)20 to test the pairing symmetry. Details of our tricrystal experiments have been reported elsewhere3'4'8'21'22. The SSM used in this experiment mechanically scans a sample with respect to a high-spatial-resolution, low-Tc integrated SQUID magnetometer so that the pickup loop is primarily sensitive to the z-component of the sample magnetic field, with a







spatial resolution set by the size of the pickup loop. The SQUID magnetometer has an 8.2-u.m diamond-shaped pickup loop with 0.8-u,m linewidths and well shielded leads. Calibration of the magnetic field intensities in the tricrystal experiment geometry has been performed in a number of different ways which agree with each other to within -10% (ref. 21). Figure 3 shows







a three-dimensional rendering of an SSM image of the T12201 blanket film deposited on a (100) SrTiO3 substrate with the geometry of Fig. 1. There is only one magnetic vortex trapped in the 170 X 230 |xm field of view, at the bicrystal meeting point. Figure 4 shows cross-sections through the wedge point of the SSM image of Fig. 3 along the directions OA (curve a) and OB







(curve b) as defined in Fig. 1. The observed field distribution was modelled as described in ref. 22; the surface fields of a Josephson vortex were propagated to the height of the pickup loop using Fourier transform techniques, and then integrated over the known pickup loop geometry. The close agreement between modelling and experiment for both wings of the vortex







shows that this is indeed a h/4e half-flux quantum and that the flux distribution is very symmetric, as designed. There is only the half-flux quantum trapped in a relatively large area, suggesting that this is spontaneously generated flux, as expected for the ground state of a superconducting loop with an odd number of sign changes in the pair tunnelling current. The







magnetic flux trapped at the wedge tip is evenly and symmetrically distributed, with no extra flux spreading along the OM or OM'directions, showing that the grain boundaries OM and OM' are strongly coupled: the sample acts as a bicrystal as intended. The order parameter should transform in accordance with the symmetry operations of the relevant crystal point group. For







a tetragonal system with point group C4v such as T12201, s- and d-wave pair states correspond to two distinctly different irreducible representations Alg and Big respectively. An admixture of s and d is not allowed. Therefore the observation of the half-integer flux quantum effect in this geometry represents a definitive, model-independent pair tunnelling evidence for







pure d_yi pairing symmetry. Although the present experiment cannot distinguish between the dj_f and dxy states, dxy symmetry has been ruled out by photoimission23'24. Our results can also unambiguously rule out symmetry-independent mechanisms, such as spin-flip tunnelling at the grain boundary, for the half-flux quantum effect. Such a mechanism would not have a sign







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