  Using scanning tunneling spectroscopy we have investigated the spatial
evolution of the anomalous c-axis zero bias conductance peak, discovered in a
previous study by our group, in epitaxial La$_{1.88}$Sr$_{0.12}$CuO$_4$ thin
films. We found an anisotropic spatial dependence of the corresponding
low-energy density of states which complies with the predicted spectral
features of an anti-phase ordering of the d-wave order parameter within the
ab-plane. Such an ordering was recently suggested to account for the 1/8
anomaly in the high temperature superconductors and the dynamical layer
decoupling recently reported to occur in the transport studies of
La$_{15/8}$Ba$_{1/8}$CuO$_4$.
