Generalization of interlayer tunneling models to cuprate superconductors with charge density waves

At the beginning of cuprate superconductors, the interlayer tunneling (ILT) and Lawrence-Doniach (L-D) models, which connect the CuO planes by Josephson coupling were considered the leading theoretical proposals for these materials. However, measurements of the interlayer magnetic penetration depth $\lambda_{c}$ yielded larger values than required by the ILT model. After the discovery of planar stripes and incommensurate charge ordering, it was also possible to consider Josephson coupling between these mesoscopic charge domains or blocks. We show that the average intralayer is larger than the interlayer coupling and comparable with the condensation energy, leading to a superconducting transition by long-range phase order. Another consequence is that the ratio $[\lambda_{c}/\lambda_{ab}]^2$ is directly proportional resistivity ratio $\rho_c/ \rho_{ab}$ near the superconducting transition temperature in agreement with several measurements.