Phase-sensitive mapping of electronic wavefunctions in atomically precise nanostructures*

We use a custom-built scanning tunneling microscope (STM) to assemble atomically precise nanostructures and to study the evolution of engineered electronic wavefunctions. We investigate resonant structures of different geometries constructed from individual atoms and molecules at 4 K. STM measurements directly probe wavefunction probability density but can indirectly provide information about quantum-mechanical phase. Through controlled quantum interference we thus use the STM as a phase-sensitive probe of single electron wavefunctions formed from the two-dimensional electron gas on the Cu(111) surface. By varying constraints imposed by symmetry, the boundary geometry, and relative or statistical phase (e.g. via magnetism or field effects), we can tune and elucidate energy and phase information of specific electronic quantum states. This level of detection and control is critical for new technologies based on few-electron devices.