Shell and supershell structures of nanowires, a quantum-mechanical analysis

The stability of sodium nanowires is studied by modeling them as infinite uniform jellium cylinders and solving self-consistently for the electronic structure. The total energy per unit length oscillates as a function of the wire radius giving a shell structure. The amplitude of the energy oscillations attenuates regularly, reflecting a supershell structure. We compare our theoretical results with recent experiments [A. I. Yanson et al., Nature 400, 144 (1999); Phys. Rev. Lett. 84, 5832 (2000)] performed by the mechanically controllable break junctions (MCB) technique. The comparison clarifies the origin of the observed shell structure and especially the formation of the quantum beats of the supershell structure and supports the conclusions based on an earlier semiclassical model. The comparison is also a quantitative test for the reliability of the simple stabilized-jellium model as well as for the accuracy of the equation used to relate the conductivity and the area of the narrowest point of the constriction.