Observation of shell structure in sodium nanowires

The quantum states of a system of particles in a finite spatial domain in general consist of a set of discrete energy eigenvalues; these are usually grouped into bunches of degenerate or close-lying levels, called shells. In fermionic systems, this gives rise to a local minimum in the total energy when all the states of a given shell are occupied. In particular, the closed-shell electronic configuration of the noble gases produces their exceptional stability. Shell effects have previously been observed for protons and neutrons in nuclei and for clusters of metal atoms. Here we report the observation of shell effects in an open system - a sodium metal nanowire connecting two bulk sodium metal electrodes, which are progressively pulled apart. We measure oscillations in the statistical distribution of conductance values, for contact cross-sections containing up to a hundred atoms or more. The period follows the law expected from shell-closure effects, similar to the abundance peaks at `magic numbers' of atoms in metal clusters.Comment: The argumentation in favour of shell structure owing to the fluctuations in the free energy of the nanowires has been strengthened. Further improvements in the presentation include the plot of the radius of the wires versus shell number in Fig.