Stability and symmetry breaking in metal nanowires: The nanoscale free-electron model

A general linear stability analysis of simple metal nanowires is presented using a continuum approach that correctly accounts for material-specific surface properties and electronic quantum-size effects. The competition between surface tension and electron-shell effects leads to a complex landscape of stable structures as a function of diameter, cross section, and temperature. By considering arbitrary symmetry-breaking deformations, it is shown that the cylinder is the only generically stable structure. Nevertheless, a plethora of structures with broken axial symmetry is found at low conductance values, including wires with quadrupolar, hexapolar, and octupolar cross sections. These nonintegrable shapes are compared to previous results on elliptical cross sections, and their material-dependent relative stability is discussed.