Symmetry of the superconducting order paramete

More than 15 years studies of high temperature superconductivity in cuprates accumulated many evidences of the d-wave type symmetry of the superconducting order parameter (OP) in these materials. The most strong ones has been found from the ARPES experiments [1], quantum interference... 

Fig. 11.13. Experimental observations of (T = 4.2 K) as a function of misorientation angle from the results of several groups [11.1-11.3] show an exponential dependence. Where the results were reported at E = 77 K, the values at 4.2 K were extrapolated from the temperature dependence of Jq [11.45]. The grain boundary tunneling current calculated from eq. 11.2 using the grain boundary widths from Fig. 11.12 shows excellent quantitative agreement for a width defined by a copper(I) valence between 1.5 and 1.9. This copper valence corresponds to the copper(I) valence in bulk YBCO when it becomes non-superconducting. The predicted drop in due to the symmetry of the superconducting order parameter is insufficient by two orders of magnitude to account for the observed behavior.

The residual absorption found in the vast majority of cuprates is not consistent with s-wave symmetry of the superconducting order parameter. Since the DOS inside the gap region of an s-wave superconductor is exactly zero at T = 0, the dissipative part of the conductivity must vanish for a) < 2A, in clear contrast with the experimental data. There have been several attempts to explain the residual absorption in the superconducting state assuming d-wave symmetry. In a d-wave superconductor, the DOS is finite at all finite... 

During the last several years, a great deal of effort has been expended to determine the symmetry of the superconducting order parameter of the high-Tc cuprate superconductors... 

Here, yr is the superconductor gap order parameter. It corresponds to the wave function of the superconducting pair in BCS theory and has the X Y symmetry of the smectic order parameter. The magnetic vector potential A comes analogous to the director n (m and e are the mass and charge of a single electron, fi Planck s constant, c the velocity of light and jU the magnetic permittivity). 

It is important to emphasize (see Ref. [2]) that the TC in this case differs from the TC realized in the superfluid He3 and, for example, in materials like Sr2RuC>4 [4], The triplet-type superconducting condensate we predict here is symmetric in momentum and therefore is insensitive to non-magnetic impurities. It is odd in frequency and is called sometimes odd superconductivity. This type of the pairing has been proposed by Berezinskii in 1975 [5] as a possible candidate for the mechanism of superfluidity in He3. However, it turned out that another type of pairing was realized in He3 triplet, odd in momentum p (sensitive to ordinary impurities) and even in the Matsubara frequencies w. It is also important to note that while the symmetry of the order parameter A in Refs. [4, 5] differs from that of the BCS order parameter, in our case A is nonzero only in the S layers and is of the BCS type. It is determined by the amplitude of the singlet component. Since the triplet and singlet components are connected which each other, the TC affects A in an indirect way. 

Many physical properties of superconducting materials are directly determined by the syrrrme-try of the SC order parameter. The possible types of order parameters are restricted by crystal symmetry. This fact provides a classification scheme for differerrt supercorrducting states and, in addition, allows one to constract the superconducting classes by mearts of group theory. 

As a possible explanation of this phenomenon the authors consider, in the case of non s-wave pairing, the coupling between the superconducting order parameter with an environment of different symmetry and propose that it may lead to two different Tc s dependent on the crystallographic direction. Thus, T, which changes with the chain oxygen, may be the transition temperature for c-axis superconductivity while Td, which seems rather independent of oxygen, may be the transition temperature for the superconductivity of the planes. 

On the other hand, microwave penetration depth (Anlage et al. 1994) and Raman spectroscopy measurements (Stadloper et al. 1995) on the electron-doped superconductor Ndi 85Ceo.i5Cu04-, indicate that the superconducting order parameter of this material has s-wave symmetry. 

We now study the characteristics of the order parameter of the superconductivity induced by the attractive interaction between the flu electrons originated in the dynamic Jahn-Teller effect. To this end, we estimate the energy gain per Cgo molecule due to the superconductivity by using a simple consideration of Hint. It is reasonable to expect that there can be three types of order parameter, i.e., those of the Ag, Hg, and TXg symmetries, because flu X qu is reduced to the sum of these three representations. We examine the three possibilities below. 

As expected from the above consideration, it is most likely that the order parameter of the superconductivity in A3C6o is of the Ag symmetry and spin-singlet. We confirm this by constructing the BCS wavefunction of the Ag type, P), as follows ... 

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