Credit: © 2008 H. Manoharan/Stanford University

The ability of the scanning tunnelling microscope (STM) to manipulate and probe matter at the level of single atoms and molecules has been established for almost two decades. However, physicists can always find new tricks to perform, as Hari Manoharan and co-workers1 at Stanford University now demonstrate by determining the quantum phase of the wave function of a nanostructure without recourse to interferometry.

Manoharan and co-workers begin by using a homemade STM operating at 4.2 K to move carbon monoxide molecules around a copper surface to make three different nine-sided figures known as the Bilby, Hawk and Broken Hawk (see image). All three figures are composed of seven identical triangles that are arranged so that they have the same area and perimeter. Moreover, two are designed so that they are isospectral — that is, they both have the same electronic structure even though their shapes are different.

The Stanford team then uses the STM to probe the wave function of the electrons confined within the nanostructures. Normally it is only possible to determine the amplitude of the wave function with this approach, but Manoharan and co-workers exploit the isospectral properties of the shapes to determine the phase as well. The team also repeats this feat with more complicated shapes called the Aye-aye and the Beluga, which are made of 21 identical triangles each.