Force, charge, and conductance of an ideal metallic nanowire

The conducting and mechanical properties of a metallic nanowire formed at the junction between two macroscopic metallic electrodes are investigated. Both two- and three-dimensional wires with a wide-narrow-wide geometry are modeled in the free-electron approximation with hard-wall boundary conditions. Tunneling and quantum-size effects are treated exactly using the scattering matrix formalism. Oscillations of order $E_F/{\lambda }_F$ in the tensile force are found when the wire is stretched to the breaking point, which are synchronized with quantized jumps in the conductance. The force and conductance are shown to be essentially independent of the width of the wide sections (electrodes). The exact results are compared with an adiabatic approximation; the latter is found to overestimate the effects of tunneling, but still gives qualitatively reasonable results for nanowires of length $L\gg {\lambda }_F,$ even for this abrupt geometry. In addition to the force and conductance, the net charge of the nanowire is calculated and the effects of screening are included within linear response theory. Mesoscopic charge fluctuations of order e are predicted that are strongly correlated with the mesoscopic force fluctuations. The local density of states at the Fermi energy exhibits nontrivial behavior that is correlated with fine structure in the force and conductance, showing the importance of treating the whole wire as a mesoscopic system rather than treating only the narrow part.