Tip orbitals and the atomic corrugation of metal surfaces in scanning tunneling microscopy

Abstract

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 ${\ensuremath{\Delta}}_{l,m}(R).$ Results show that the corrugation, observed over the wide range ${(10}^{5}\ensuremath{-}{10}^{8}\ensuremath{\Omega}),$ 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 ${\ensuremath{\Delta}}_{l,m}(R).$ 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 ${d}_{{x}^{2}\ensuremath{-}{y}^{2}},$ 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.