Effect of Transparency on the Josephson Junction between D-wave Superconductors

In this paper, a dc Josephson junction between two singlet superconductors (d-wave and s-wave) with arbitrary reflection coefficient has been investigated theoretically following the famous paper [ Y. Tanaka and S. Kashiwaya 1996 Phys. Rev. B 53, R11957]. For the case of High Tc superconductors, the c-axes are parallel to an interface with finite transparency and their ab-planes have a mis-orientation. The effect of transparency and mis-orientation on the currents is studied both analytically and numerically. It is observed that, the current phase relations are totally different from the case of ideal transparent Josephson junctions between d-wave superconductors and two s-wave superconductors. This apparatus can be used to demonstrate d-wave order parameter in High Tc superconductors. PACS numbers: 74.50.+r,85.25.Cp,74.20.Rp,85.25.Dq,74.78.Bz The quantum transport through the junctions between high Tc unconventional superconductors has attracted much attention in recent years, particularly in view of various recently discovered copper oxide compounds. It is well-known that the isotope effect for these superconductors is rejected or weak. The isotope effect is the most important reason for the phonon participation in the superconductivity mechanism. Thus we should search for another pairing mechanism for high-Tc superconductors. In spite of enormous efforts made to understand the physical mechanisms of pairing in various highTc superconductors, the situation still remains unclear. A central role in understanding of this type of superconductivity relates to the symmetry of the order parameter. Soon after the first Bednords and Muller [1] discovery, the symmetry of the dx2−y2-form was suggested for high-Tc superconducting materials. It was considered that the formation of midgap states (MGS) at surfaces and interfaces of d-wave superconductors affects the current transport properties of junctions involving d-wave superconductors [2]. It is found that in spite of s-wave superconductors for d-wave superconductors we can observe midgap states. This phenomenon is due to the changing the sign of order parameter in d-wave superconductors. On the other hand, measurements of direct Josephson current yield valuable information on the symmetry of the order parameter which is essential for understanding the mechanisms of superconductivity in these complex materials. Phase interference experiments definitely suggest the presence of d-wave symmetry of the order parameter in high-Tc superconductors [3, 4]. The properties of spontaneous currents generated at surfaces and interfaces of d-wave superconductors using the selfconsistent quasiclassical Eilenberger equations are investigated [5]. The effect of transparency and mis-orientation on the current as the main purpose of this paper. In this paper, we have solved the nonlocal Eilenberger equations [6] supplemented with Zaitsev boundary conditions [7] and obtained the corresponding Green functions analytically. These boundary conditions have been rewritten in [8, 9]. Then, using the Green functions, we compute the spontaneous and Josephson currents. The system which is investigated in this paper, consists of two d-wave superconductors connecting through an interface. The interface has the finite transparency for quasiparticles and two superconductors have a mis-orientation with each other. Quasiclassical theory of superconductivity is based on the nonlocal Eilenberger’s equations for the quasiclassical matrix propagator. In the case of a clean (ballistic) singlet anisotropically paired superconductor, the equations for the ξ-integrated Green functions reduce to the following 2× 2 matrix form [6] vF · ∂ ∂r Ĝω(vF , r) + [ωτ̂3 + ∆̂(vF , r), Ĝω(vF , r)] = 0 (1) Effect of Transparency on the D-wave Josephson Junction 2 0 0.25 0.5 0.75 1 φ/2π -0.1 0 0.1 0.2 0.3 j J / j 0 l=0.0, r =0.0 l=0.0, r =22.5 l=0.0, r =45 l=0.0, r =67.5 l=0.0, r =90 α