Universality of scanning tunneling microscopy on cuprate superconductors*

We consider the problem of local tunneling into cuprate superconductors, combining model based calculations for the superconducting order parameter with wavefunction information obtained from first principles electronic structure. We use a recently developed Wannier function based method to calculate topographies, spectra, conductance maps and normalized conductance maps close to impurities. We find that it is the local planar Cu d_{x^2-y^2} Wannier function, qualitatively similar for many systems several Angstrom above the surface, that controls the form of the tunneling spectrum and the spatial patterns near perturbations. In particular, we discuss why STM results on BSCCO and NaCCOC are essentially identical.