D-wave pairing

By plotting a against temperature for the four fields studied,9 H = 0.05, 1.0, 3.0 and 6.0 Tesla, one finds qualitatively similar features to previous data (see e.g., Ref. 10), but also certain features that rule out d-wave pairing, and which provide clues regarding the extrinsic effects (i.e., effects not directly associated with the gap function symmetry) that play a role in shaping them. Specifically, these data show (i) a distinctive inflection point in cr(T,H) versus temperature near T 20 K, which is most evident at intermediate fields (i.e., H=1.0 and 3.0 Tesla), and is reminiscent of earlier data on Bi2Sr2CaCu20g,4 and (ii) a non-monotonic dependence of the quantity 0,H) on applied magnetic field H. These two effects cannot be adequately explained with either an. v-wavc or a d-wave model alone. 

Experiments utilizing microwave cavity resonance, uc susceptibility, or rf resonance12 have been executed on YBa2Cu307 to test theoretical predictions of d-wave pairing theory for the non-linear Meissner effect.13 The predicted effects turned out to be either absent or unobservably small. Moreover, the predicted four-fold symmetry in the ab plane for the d(.x2 — y2 ) order parameter is also absent.14... 

From the data and analyses presented, and the comparison with the nonlocal d-wave theory of Ref. 10, it is clear that there is no evidence in any of the /u+SR data for d-wave pairing. All of the data are, however, completely consistent with temperature-activated vortex de-pinning that masks an under-... 

YBa2Cu307 is clearly an s-wave superconductor as demonstrated convincingly by the measurements of Harshman et al. [10], Once temperature-activated and field-dependent flux-line disorder are accounted for, the data are fully consistent with s-wave pairing. These data also rule out d-wave pairing. 

It was shown that the temperature dependence of the specific heat of the spin-fluctuations mechanism in cuprate superconductors proportional to square the temperature, which correspond d wave pairing [6,9]... 

There seems to be a growing consensus that the superconductivity is d-wave [97], more specifically, dx2 y2 type. Recent microwave measurements [98] would indicate that the penetration depth is linear in temperature, a sign that the gap has zeros. As pointed out in Ref. 99, this does not exclude 5-wave pairing since harmonics of the basic combinations [Eq. (38)] can also lead to zeros of the gap on the Fermi surface. It is interesting to note that d-wave pairing is quite in line with the extrapolations of the two-dimensional Hubbard and t-J models (Section V.B) and the observed competition with AFM. This would point to a spin-exchange mechanism. The parallel with the quasi-one-dimensional superconductors is striking. 

For the d-wave pairing case, strong impurity scattering destroys the superconductivity itself. The Knight-shift measurement provides the change of Xs most accurately. However, to distinguish. v or d from the temperature dependence of K is not easy because at low temperatures the dependence is easily affected by impurities in r/-wave pairing, as discussed later. 

From the temperature dependence of 1/7) for Cu in YBCO7, which is similar to that in HF materials (no coherence peak and 7 3-like dependence), together with the decrease in K below Tc, d-wave pairing was originally proposed by Kitaoka et al42... 

Ti has no coherence peak, followed by a sharp decrease below Tc. The large linear part, associated with the pair-breaking effect due to the imperfection of the crystal, is seen in the lower- Tc crystals. The relation between Tc and Nres agrees well with the theory as shown in Fig. 18 where To = 1.5 K is adopted, consistent with the present high-T crystals. In high-T( crystals, the T3 behaviour has been observed below 1 K down to 0.15 K, which implies the formation of the line-node gap. The 1 jT behaviour can be well interpreted by the line-node-gap model A([Pg.136]

The simplest even-parity state is the isotropic state encountered in ordinary superconductors. This state is often referred to as s-wave state . The isotropic order parameter does not depend on the direction k and reduces to a complex constant cj) = Its only degree of freedom is the Josephson phase. By far the most extensively studied examples of anisotropic pairing are the p-wave states realized in the superfiuid phases of He, the d-wave pair state in high-Tc superconductors and the f-wave states in UPts and SrRu204. The odd parity (p, f) states among these examples are characterised by more than one order parameter component with internal phase degrees of freedom which appear in addition to the overall Josephson phase. 

Comer-junction experiments by other groups (Brawner and Ott 1994, Mathai et al. 1995, Miller et al. 1995) and tricrystal ring experiments (Tsuei et al. 1994, Kirtley et al. 1995) also provide evidence for d-wave pairing symmetry. 

Various mixed s- and d-wave pairing models that have been developed to account for the superconducting properties of the orthorhombic YBCO-123 system are reviewed by Beal-Monod (1998). 

Fig. 22. Temperature dependence of the normalized spin susceptibility in gadolinium-doped YBajCttjOg vs. the reduced temperature. The spin susceptibility has been determined from Gd g-shift measurements at high frequencies. The solid line indicates a fit to a model assuming d-wave pairing symmetry. The dashed lines represents the results for s-wave superconductivity in the weak coupling limit. From Janossy et al. (1997).

The final approach used for spin fluctuations is a semi-phenomenological theory which takes the observed dynamic susceptibility, uses this as a model to construct a pair potential, and then tries to solve for for real systems. This approach was first advocated by Miyake et al. (1986), who observed that the spin fluctuations in heavy fermions were of an antiferromagnetic nature, as opposed to the ferromagnetic nature seen in He. This leads to d-wave pairing for a simple lattice [see Scalapino et al. (1986, 1987) and Beal-Monod et al. (1986) for related approaches]. A nice review of the physics behind these models can be found in Pethick and Pines (1987), which is highly recommended reading. 

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