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 jc(T ) for sand 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 jc(T ) ∝ T at low T . By parameterizing our theory with c-axis resistivity data from YBa2Cu3O7−δ (YBCO), we estimate jc(T ) for optimally doped and underdoped members of this family. jc(T ) can be measured either directly or indirectly through microwave penetration depth experiments, and current measurements on Bi2Sr2CaCu2O8