ORIGIN OF INTRINSIC JOSEPHSON COUPLING IN THE CUPRATES AND ITS RELATION TO ORDER-PARAMETER SYMMETRY - AN INCOHERENT HOPPING MODEL

Experiments on the cuprate superconductors demonstrate that these materials may be viewed as a stack of Josephson junctions along the direction normal to the CuO2 planes (the c-axis). In this paper, we present a model which describes this intrinsic Josephson coupling in terms of incoherent quasiparticle hopping along the c-axis arising from wave-function overlap, impurity-assisted hopping, and boson-assisted hopping. We use this model to compute the magnitude and temperature T dependence of the resulting Josephson critical current j(c)(T) for s- and d-wave superconductors. Contrary to other approaches, d-wave pairing in this model is compatible with an intrinsic Josephson effect at all hole concentrations and leads to j(c)(T) proportional to T at low T. By parameterizing our theory with c-axis resistivity data from YBa2Cu3O7-delta (YBCO), we estimate j(c)(T) for optimally doped and underdoped members of this family. j(c)(T) can be measured either directly or indirectly through microwave penetration depth experiments, and current measurements on Bi2Sr2CaCu2O8 and La2-xSrxCuO4 are found to be consistent with s-wave pairing and the dominance of assisted hopping processes. The situation in YBCO is still unclear, but our estimates suggest that further experiments on this compound would be of great help in elucidating the validity of our model in general and the pairing symmetry in particular.