Estimation of the surface-d to bulk-s Crossover in the Macroscopic Superconducting Wavefunction in Cuprates

The concept of a surface d- and bulk s-symmetry in cuprate superconductors is applied to recent small-angle neutron-scattering results. These show a change of hexagonal to square vortex lattice as a function of the magnetic field along the c-axis. Identifying the hexagonal lattice with s- and the square with d-symmetry, the crossover distance from the surface d to the bulk s perpendicular to the c-axis is estimated to be 35 nm for LSCO and roughly 7 nm for YBCO, both at optimum doping. The crossover along the c-axis has to be of only a few layers distance to reconcile tunneling, photoemission and pulsed femtosecond reflectivity experiments. These estimates are compatible with m-rotation, NMR and other experiments.