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16 Will-be-set-by-IN-TECH

At the same time, when an *s*-wave contribution to the actual order parameter in a cuprate sample is dominant up to the complete disappearance of the *d*-wave component, the *ic* (*γ*) dependences for junctions involving CDW superconductors are no longer constant as in the CDW-free case. This prediction can be verified for CDW superconductors with *a fortiori*

In this paper, our approach was purely theoretical. We did not discuss unavoidable experimental difficulties to face with in fabricating Josephson junctions necessary to check the results obtained here. We are fully aware that the emerging problems can be solved on the basis of already accumulated knowledge concerning the nature of grain boundaries in high-*Tc* oxides [37, 115–119, 122, 264–268]. Note that required junctions can be created at random in an uncontrollable fashion using the break-junction technique [250]. This method allows to comparatively easily detect CDW (pseudogap) influence on the tilt-angle dependences.

To summarize, measurements of the Josephson current between an ordinary superconductor and a *d*-wave or extended *s*-wave one (e.g., a high-*Tc* oxide) would be useful to detect a possible CDW influence on the electron spectrum of the latter. Similar studies of iron-based superconductors with doping-dependent spin density waves (SDWs) would also be of benefit (see, e.g., recent Reviews [78, 269–275]), since CDW and SDW superconductors have similar,

AIV is grateful to Kasa im. Józefa Mianowskiego, Fundacja na Rzecz Nauki Polskej, and Fundacja Zygmunta Zaleskiego for the financial support of his visits to Warsaw. The work was partially supported by the Project N 8 of the 2012-2014 Scientific Cooperation Agreement

*Institute of Physics, National Academy of Sciences of Ukraine, 46, Nauka Ave., Kyiv 03028, Ukraine*

*Institute of Physics, Polish Academy of Sciences, 32/46, Al. Lotników, PL-02-668 Warsaw, Poland*

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© 2012 Kato et al., licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2012 Kato et al., licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

φ

φ

of the superconducting order

Δ= Δ *<sup>i</sup> e* . This phase causes interference

**Composite Structures of d-Wave and s-Wave** 

**Superconductors (d-Dot): Analysis Using Two-**

Masaru Kato, Takekazu Ishida, Tomio Koyama and Masahiko Machida

Superconductivity is a macroscopic quantum phenomenon [1]. Therefore it shows quite interesting properties because of its quantum nature. Such properties are described by a macroscopic complex wave function of the superconductivity. Especially, a phase of the macroscopic wave function play an important role in these properties. For example, superconducting devices, such as, superconducting charge, flux and phase qubits, superconducting single flux quantum device, and intrinsic Josephson junction Terahertz emitter of high Tc cuprate superconductors, use such quantum nature of superconductivity.

effect, such as, Josephson effect, and quantization of vortices in the superconductor. But unconventional and anisotropic superconductivity have different phase that comes from internal degree of freedom of the superconducting order parameter. Because in the superconductors, electrons are paired and if their paring symmetry is an s-wave, as in the conventional superconductors, the order parameter is just a single complex number. But if the symmetry is other one such as p-wave or d-wave, then the order parameter has an internal phase [2,3]. For example, d-wave superconductors, especially 2 2 *<sup>x</sup>* <sup>−</sup> *<sup>y</sup> d* -wave superconductors have a symmetry that is shown in Fig. 1. This symmetry is internal and it appears in momentum space that means the wave function of the Cooper pair moving along the x-axis has + sign and that moving along y-axis has – sign. This is also another phase of superconducting order parameter and it affects the interference phenomena in the

**Component Ginzburg-Landau Equations** 

Additional information is available at the end of the chapter

They have attracted much attention recently.

parameter or the macroscopic wave function

In conventional superconductors, there is only single phase

http://dx.doi.org/10.5772/51550

**1. Introduction** 

superconductors.
