Conductance quantization and electron resonances in sharp tips and atomic-size contacts

The electronic and transport properties of atomic-size contacts are analyzed theoretically using a self-consistent tight-binding model. Our results show that, for s-like metals, a sufficiently narrow contact exhibits well defined resonant states at the Fermi energy, spatially localized in the neck region. These states are robust with respect to disorder and provide a simple explanation for the observed tendency to conductance quantization. It is also shown that these properties disappear for a sufficiently large contact area. The possible relevance of the resonant states in scanning tunneling spectroscopy using sharp tips is briefly discussed.