  Quasicrystals possess long-range order but lack the translational symmetry of
crystalline solids. In solid state physics, periodicity is one of the
fundamental properties that prescribes the electronic band structure in
crystals. In the absence of periodicity and the presence of quasicrystalline
order, the ways that electronic states change remain a mystery. Scanning
tunneling microscopy and atomic manipulation can be used to assemble a
two-dimensional quasicrystalline structure mapped upon the Penrose tiling.
Here, carbon monoxide molecules are arranged on the surface of Cu(111) one at a
time to form the potential landscape that mimics the ionic potential of atoms
in natural materials by constraining the electrons in the two-dimensional
surface state of Cu(111). The real-space images reveal the presence of the
quasiperiodic order in the electronic wave functions and the Fourier analysis
of our results links the energy of the resonant states to the local vertex
structure of the quasicrystal.
