The surface order parameter symmetry of highly twinned YBCO crystals

Josephson tunneling between YBa₂Cu₃O _7−δ and Pb with the current flowing along the c-axis of the YBa₂Cu₃O_7−δ is presumed to come from an s-wave component of the superconductivity in YBa₂Cu ₃O_7−δ. Experiments on multi-twin samples are not entirely consistent with this hypothesis. The sign changes of the s-wave order parameter across the N_T twin boundaries should give cancellations, resulting in a small ($NT$) tunneling current. The actual current is larger than this. A theory of this unexpectedly large current based upon a surface effect is proposed. Disorder-induced suppression of the d-wave component at the (001) surface leads to s-wave coherence across the twin boundaries and a non-random tunneling current. The possible causes of such d-wave surface suppression are discussed. The effect of a distribution of twin sizes is explored and the case of an ordered array of d + s and d − s twins is then solved. The estimated twin size at which s-wave surface coherence occurs is consistent with typical sizes observed in experiments. In this picture, there is a phase difference of π/2 between different surfaces of the material. A corner junction experiment to test this picture is proposed.