In the presence of an elastic barrier at both interfaces of a mesoscopic d-wave superconductor–normal-metal–d-wave superconductor (DND junction), the Josephson current at zero temperature is studied by using a simple matrix method. As a limiting case, the tunneling between two d-wave superconductors coupled by a insulator barrier (DID structure) is particularly addressed. The effects of sign change and anisotropic gap structure of the ${\mathit{d}}_{{\mathit{x}}^2\mathrm{-}{\mathit{y}}^2}$ superconductor are carefully considered in the Andreev reflection. The coupling of forward-moving quasiparticles and backward-moving quasiparticles with different pair potentials leads to contrasting Andreev spectra in different motion angle regions, which is specific to our model. Unlike conventional superconducting point-contact junctions, the conduction crossing the Fermi surface plays an important role in determining the critical current. Our theoritical results suggest that the dependence of the critical current on the grain boundary tilt angle provides a clue to identify the pairing symmetry of high-${\mathit{T}}_{\mathit{c}}$ superconductors. © 1996 The American Physical Society.

• Received 28 May 1996

DOI:https://doi.org/10.1103/PhysRevB.54.12509