Electronic Size Effects in Three-Dimensional Nanostructures

We show that bismuth nanostructures form three-dimensional patterns governed by two-dimensional electronic effects. Scanning tunneling microscopy reveals that both the vertical and the lateral dimensions of the structures strongly favor certain values and that the preferred widths are substantially different for each preferred height. First-principles calculations demonstrate that this vertical-lateral correlation is governed by the Fermi surface topology and that this is itself sensitively dependent on the dimensions of the structure.