When atomic resolution is achieved, the scanning tunneling microscope (STM) image of a dense metal surface shows a giant amplitude, i.e., between one and two orders of magnitude larger than expected from an s-wave tip. To date, no satisfactory explanation has been given. Using our earlier nonperturbative formalism for the tunnel current, we reconsider the corrugation problem with a single atom tip having s, p, or d orbitals, or a combination. Particular emphasis is on the value of the corrugation as a function of the tunnel resistance ${\Delta }_{l,m}\mathrm{}\left(R\right).$ Results show that the corrugation, observed over the wide range ${(10\mathrm{}}^5-{10}^8\Omega ),$ is inconsistent by nearly two orders of magnitude with the s-orbital theory, and by one order of magnitude with the $d_{z^2}$ one. We also can put aside tip-surface interactions. Tip states, such as $p_z$ and $d_{z^2},$ give basically s-wave behavior in ${\Delta }_{l,m}\mathrm{}\left(R\right).$ However, those with axial symmetry, such as $d_{\mathrm{xz}}{+id}_{\mathrm{yz}}$ and having a nodal line orthogonal to the surface, give an enhanced corrugation. Finally, in tip states with a nodal plane, such as $d_{x^2-y^2},$ the enhancement effect is much more pronounced. Identical results are obtained by considering separately the nearly free electron model, and a new method of atomic orbital superposition, for the metal surface.

• Received 27 July 1999

DOI:https://doi.org/10.1103/PhysRevB.61.7656