We give a consistent explanation of the c-axis Josephson tunneling experiment by Sun and co-workers between YBa 2 Cu 3 O 6ϩx and Pb within the d-wave pairing scenario. Using a Ginzburg-Landau formulation, orthorhombic deformation and twinning of the crystal lattice are taken into account. In the presence of orthorhombic distortion, symmetry arguments allow a c-axis Josephson coupling between YBa 2 Cu 3 O 6ϩx and Pb. However, for a highly twinned YBa 2 Cu 3 O 6ϩx sample, the Josephson coupling is weakened due to destructive interference effects. On the other hand, we demonstrate that destructive effects due to twinning can be overcome, if twin boundaries support a state which locally breaks time reversal symmetry and leads to a channel which adds constructively to the total Josephson coupling. Properties of the Josephson junctions measured in experiment, such as the Fraunhofer pattern and the Fiske resonance, keep their standard form for such a junction. The existence of a twin boundary state with broken time reversal symmetry can directly be tested, for example, by observing vortices with fractional flux quanta on twin boundaries.

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