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 c-direction. 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) \propto T at low T. By parameterizing our theory with c-axis resistivity data from YBCO, we estimate j_c (T) for optimally doped and underdoped members of this family. 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. We also discuss the implications of our model for LSCO and BSCCO. 
R. J. Radtke and K. Levin