D-wave Model Research Articles

Antiferromagnetic spin correlation and superconductivity in the overdoped superconductor La 2− xSr xCuO 4

In the overdoped region of x=0.20−0.24 in La 2− x Sr x CuO 4, the rapid decrease in 1 T 1 and the Knight shift just below T c have been observed as well as in the lightly doped region of x⩽0.15, verifying the presence of superconducting phases even in the overdoped region from a microscopic level. At low T, a gapless feature of superconductivity has been found from the characteristic behavior of a T 1 T=constant law and the presence of the residual spin Knight shift. This behavior of T 1 and the Knight shift are explained in terms of a d-wave model in which a finite residual density of states is taken into account at the Fermi level associated with a pair-breaking effect.

Effect of d-wave energy-gap symmetry on Raman shifts.

We have calculated the shift and change in width, due to superconductivity, for a q=0 Raman-active phonon in a two-dimensional, tight-binding band structure with a d-wave pairing interaction. We find that additional structure appears in the phonon self-energy due to the van Hove singularity, which occurs in two dimensions. A more general model of a superconductor with nodes in the gap function is also examined and related to both the d-wave model and another model for layered superconductors. In contrast to the usual isotropic s-wave case where a phonon with frequency less than twice the gap value is softened and narrowed, we find softening with broadening in these models. Comparison of the anisotropic models is made with experiment.

NMR and NQR studies of spin dynamics and superconductivity in High-T c oxides

The magnetic and superconducting properties in the high-T c cuprates have been investigated over a wide hole doping range by63Cu,17O and205Tl NMR and NQR in the lightly-doped La2−xSrxCuO4 (LSCO), the heavily-doped Tl2Ba2CuO6+y (TBCO) and the Zn-doped YBa2Cu3O7 (YBCO7). In low doping region, the large antiferromagnetic (AF) spin correlation around the zone boundary (q=Q) causes the Curie-Weiss behavior of63(1/T 1 T) associated with that of the staggered susceptibility χO(T) in LSCO. In the vicinity of the hole content whereT c has a peak, the AF spin correlation still survives, although the magnetic coherence length ξM is considerably short being presumably (ξM/a) ∼ 1. The further doping destroys progressively the AF spin correlation, which is no longer present is non-superconducting TBCO compounds. These NMR evidences signify that there is an intimate relation between the presence of the AF spin correlation and the onset of the superconductivity. The local collapse of AF spin correlation is a primary cause for the unexpected strong reduction ofT c in case of the substitution of Zn impurities into the CuO2 plane. The superconducting properties clarified by NMR experiments cannot be accounted for by the conventional BCS model or other isotropic s-wave models. A d-wave model is applicable in interpreting consistently most of the NMR results, if the finite density of states at the Fermi level is taken into consideration and is associated with the pair breaking effect. There are increasing evidences that the magnetic mechanism for the superconductivity is promising in high-T c cuprates.

63Cu and17O NMR studies on the magnetic and superconducting properties of YBa2Cu3O7−y

Results of63Cu and17O NMR experiments in YBa2Cu3O7 and YBa2Cu3O6.63 are reviewed. The normal state data revealed two important aspects of the magnetic properties of these materials, namely, the temperature dependent antiferromagnetic Cu spin correlations and the spin gap behavior, the latter being observed in the reduced oxygen material. These features appear to be the general properties of many high-T c cuprates. Anomalous temperature dependence of the anisotropy of the Cu relaxation rate was found in the superconducting state of YBa2Cu3O7, which can be explained by a d-wave pairing model.

NMR and NQR studies of superconductivity in heavily doped Tl 2Ba 2CuO 6+y with a single CuO 2 plane

The superconducting property of Tl 2Ba 2CuO 6+y (TBCO) with T c =72, 40 and 0 K has been investigated by 63Cu NQR and NMR and 205Tl NMR measurements. The behaviors of the Knight shift and nuclear spin lattice relaxation time T 1 below T c have been found to be almost the same as those in YBA 2Cu 3O 7, although the behavior above T c is strongly modified in the sense that the q-dependence of the abtiferromagnetic (AF) spin fluctuation becomes less distinct upon doping. According to the argument for YBCO 7 by Ishida et al., the T-dependence of 1 T 1 and the Knight shift below T c in TBCO are well interpreted by a “gapless d-wave model” with a finite density of states at the Fermi surface. It is pointed out that impurities and imperfections and/or the applied magnetic field more or less cause the pair breaking in TBCO. Then the low- T properties in high- T c oxides are concluded to be seriously affected by the small but finite density of states at the Fermi depending on the material.

NMR study of high-T c superconductors

From systematic measurements of T c, Knight shift, NQR frequency of 63Cu and 17O with high-pressure measurement in high- T c materials, La 2−xSr xCuO 4, YBa 2Cu 3O 7 and Tl 2 Ba 2 CuO 6+ y the following results have been obtained. The staggered susceptibility at the zone boundary, χ( Q) which is a measure of the antiferromagnetic spin fluctuation decreases in order of the La, Y and Tl system. χ( Q) is governed by the number of Cu d-holes, n(Cu) and O p-holes, n(O) in the CuO 2 plane. χ( Q) increases when n(Cu)/ n(O) increases. T c increases and then decreases with n(Cu)/ n(O) having a maximum at an optimum value of n(Cu)/ n(O). Correlation between χ( Q) and T c has been discussed by assuming χ( Q) to play an essential role for the occurrence of high- T c superconductivity. The T-dependence of 1/ T 1 below T c suggests strongly the d-wave pairing model.

Nuclear relaxation and Knight shift studies of 63Cu in 90 K-and 60 K-class YBa 2Cu 3O 7−y

The nuclear relaxation rate (1/T 1) and Knight shift for Cu of YBa 2Cu 3O 7−y were measured by using the nuclear quadrupole (NQR) and magnetic resonance (NMR) techniques. For 90 K-superconductor with y∼o, 1/T 1 at the CuO 2 plane site decreases markedly without the enhancement just below T c and approximates to a T 3 behavior between 40K and 10 K. Knight shift shows a distinct decreases below T c, giving an evidence for dominant singlet pairing. For an explanation of unconventional nuclear relaxation behavior, it seems plausible to apply a d-wave model with the gap zeros of lines on the Fermi surface. For 60 K-superconductor, we found a surprising result that 1/T 1 at the CuO 2 plane site is by three order of magnitude suppressed as compared to that of 90 K superconductor and shows no anomalies at T c= 60K. This marked difference of relaxation behaviors between 90K and 60K superconductors implies a strong correlation with the mechanism of high T c superconductivity.