Stability of metal nanowires at ultrahigh current densities

We develop a generalized grand canonical potential for the ballistic nonequilibrium electron distribution in a metal nanowire with a finite applied bias voltage. Coulomb interactions are treated in the self-consistent Hartree approximation, in order to ensure gauge invariance. Using this formalism, we investigate the stability and cohesive properties of metallic nanocylinders at ultrahigh current densities. A linear stability analysis shows that metal nanowires with certain magic conductance values can support current densities up to 10¹¹A/cm² , which would vaporize a macroscopic piece of metal. This finding is consistent with experimental studies of gold nanowires. Interestingly, our analysis also reveals the existence of reentrant stability zones—geometries that are stable only under an applied bias.