  Gold nanostructures have important applications in nanoelectronics,
nano-optics as well as in precision metrology due to their intriguing
opto-electronic properties. These properties are governed by the bulk band
structure but to some extend are tunable via geometrical resonances. Here we
show that the band structure of gold itself exhibits significant size-dependent
changes already for mesoscopic critical dimensions below 30 nm. To suppress the
effects of geometrical resonances and grain boundaries, we prepared atomically
flat ultrathin films of various thicknesses by utilizing large chemically grown
single-crystalline gold platelets. We experimentally probe thickness-dependent
changes of the band structure by means of two-photon photoluminescence and
observe a surprising 100-fold increase of the nonlinear signal when the gold
film thickness is reduced below 30 nm allowing us to optically resolve
single-unit-cell steps. The effect is well explained by density functional
calculations of the thickness-dependent 2D band structure of gold.
