Kirtley and Tsuei - Physics

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996 C. C. Tsuei and J. R. Kirtley: Pairing symmetry in cuprate superconductors FIG. 21. Scanning SQUID microscope data on Bi-2212: (a) tricrystal geometry, including polar plots of assumed d x 2 y 2 order parameters aligned along the crystalline axes; (b) scanning SQUID microscope image of 640640 m 2 area of an epitaxial film of Bi-2212 on a SrTiO 3 tricrystal substrate with the geometry of Fig. 21(a), cooled in a field of 0.4 T, and imaged at 4.2 K with an 8.2-m-square pickup loop; (c) 400400 m 2 image of the same sample, cooled in nominal zero field; (d) comparison of horizontal cross sections through the images (b) and (c) with modeling assuming that all vortices have 0 of flux, except at the tricrystal point, which has 0 /2 flux spontaneously generated. structure of Bi-2212 is orthorhombic as a result of an incommensurate lattice modulation with a periodicity of 4.7b (b5.41 Å, the lattice constant) along the b-axis direction (for reviews, see Beyers and Shaw, 1988; Chen, 1992). This microstructural feature leads to a reduced Brillouin zone that is rotated by exactly /4 with respect to that of the orthorhombic YBCO. The inequivalent axes for orthorhombic anisotropy coincide with the node lines (Fig. 22) established by the ARPES measurements. From group-theoretic considerations, s-wave and d x 2 y2-wave pair states correspond to two distinct irreducible representations (i.e., A 1g and B 1g , respectively) and therefore are not allowed to mix (Annett et al., 1996). Based on this symmetry consideration, one is led to the conclusion that the s-wave component of the order parameter in Bi-2212 should be vanishingly small. This assertion is apparently supported by zero (Durosy et al., 1996; Sinha and Ng, 1998a) or nearly zero (Mössle and Kleiner, 1999) c-axis pair tunneling in this nominally orthorhombic superconducting system. Rev. Mod. Phys., Vol. 72, No. 4, October 2000
C. C. Tsuei and J. R. Kirtley: Pairing symmetry in cuprate superconductors 997 flux and circulating supercurrents at zero external field (see Fig. 15) generated by the -ring SQUID’s were quite small. Further, there was a large mutual inductance between the sample and sensor SQUID’s. Therefore the influence of the Nb-Pb sensor SQUID on the YBCO-Pb sample SQUID screening currents had to be corrected for in these measurements. Rather than measuring the amplitudes of the spontaneous flux at zero applied field, Mathai et al. measured the superconducting phase shift in their rings with a clever trick: the dependence of the screening currents in the YBCO-Pb sample SQUID’s was measured as a function of externally applied field, tracing out a number of branches, each branch corresponding to a different number of vortices in the YBCO-Pb sample SQUID. The measurements were then repeated with the leads to the Nb-Pb sensor SQUID and the external magnet reversed. This was equivalent to a time-reversal operation. If time-reversal-symmetry invariance is satisfied, and if the YBCO-Pb sample SQUID shielding current branches are labeled with the integers n, a zero ring will map under time reversal onto a branch n with nnn an even integer, while a ring will have n odd. Mathai et al. (1995) found that the ‘‘corner’’ SQUID’s had n odd while the ‘‘edge’’ SQUID’s had n even, as expected for d-wave superconductivity. Further, n was close to an integer for both types of sample SQUID’s, implying that time-reversal invariance was closely satisfied. Mathai et al. (1995) estimated that the timereversal-symmetry-breaking component of the pairing FIG. 22. Brillouin zone for Bi-2212. The reduced zone as a order parameter was less than 5%, in agreement with result of incommensurate superlattice modulation (along the b the conclusions drawn by Kirtley, Tsuei, et al. (1995) direction) is outlined schematically. The orientation of the from ‘‘magnetic titration’’ of tricrystal rings, as described in Sec. IV.C.2. These experiments had the ad- 2 y 2-wave polar plots is established by the ARPES data. vantages that they directly imaged trapped flux, so that d x its influence could be avoided; and they allowed a phase D. Thin-film SQUID magnetometry shift of to be measured self-consistently using just the ‘‘corner’’ SQUID, without reference to the ‘‘edge’’ SQUID. Later work by Gim et al. (1997) tested geometries intermediate between the ‘‘corner’’ SQUID and ‘‘edge’’ SQUID in an attempt to determine the momentum dependence of the phase shift in the order parameter. In these SQUID’s one of the junction normals was parallel to the YBCO b axis, while the other was at an angle relative to the a axis. If YBCO were a pure d-wave superconductor, these SQUID’s would be expected to have a zero phase shift for 045° and a phase shift for 45°90°. The results of these experiments were complicated by interface roughness introduced by the etching process used. However, the authors concluded that the angular dependence of the phase of the order parameter follows d x 2 y2 symmetry, although it was necessary to understand the details of the junction fabrication process to reach this conclusion. Mathai et al. (1995) performed tests of pairing symmetry in YBCO with thin-film YBCO-Pb (sample) SQUID’s. They imaged the magnetic flux in these SQUID’s as a function of externally applied magnetic field, using a scanning SQUID microscope with a low-T c Nb-Pb (sensor) SQUID. The YBCO films were epitaxially grown on (100) LaAlO 3 substrates by pulsed laser deposition. They were then patterned, a thin layer of Ag was deposited, annealed, cleaned by ion milling, and a thin Pb (In 5% at. wt) film was deposited to form SQUID’s. In the experiments of Mathai et al. (1995) the sample SQUID’s had either a ‘‘corner’’ or ‘‘edge’’ configuration, in analogy with the experiments of Wollman et al. (1993) [see, for example, Figs. 8(a) and (b)]. Also in analogy with the experiments of Wollman et al. (1993), the ‘‘corner’’ SQUID’s should be rings if YBCO is a d-wave superconductor, while the ‘‘edge’’ SQUID’s should be zero rings, independent of the superconducting pairing symmetry. The YBCO-Pb sample SQUID’s were washers, with 50-m inner-side length, and 250-m outer-side length. They had a selfinductance of about 75 pH, and a 2LI c / 0 1. This relatively small value meant that the spontaneous E. Universality of d-wave superconductivity The phase-sensitive pairing symmetry experiments described above have provided clear evidence for a pre- Rev. Mod. Phys., Vol. 72, No. 4, October 2000
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Kirtley and Tsuei - Physics

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