  Novel quantum phenomena, including high-temperature superconductivity,
topological properties, and charge/spin density waves, appear in
low-dimensional conductive materials. It is possible to artificially create
low-dimensional systems by fabricating ultrathin films, quantum wires, or
quantum dots with flat interfaces. Some experiments have been performed on
ultrathin compounds of strongly correlated electron systems. However, since it
is technically difficult to control multiple elements precisely, most of the
properties of artificially fabricated low-dimensional compounds fall into
uncharted territory. Here we show that extraordinary metal-insulator
transitions that oscillate depending on the scale occur in CaRuO_3 films with a
thickness of around several unit cells. We grow high-crystalline CaRuO_3
ultrathin films, whose surface roughness is controlled at 199 pm, by molecular
beam epitaxy. We observe that resistivity oscillates with a magic thickness of
25 {\AA}, which changes by 3 and 9 orders of magnitude at room temperature and
at low temperature, respectively. These changes are much larger than quantum
size effects. We also confirm the same periodicity with photoelectron
spectroscopy by etching the ultrathin film. Considering the large energy,
periodicity and anisotropy, we conclude that the oscillating transitions
originate from the commensurability of Mott insulation triggered by Peierls
instability arising from a dual restriction on the dimensions in wavenumber
space and real space. We have shown the possibility of producing new functional
materials by controlling film thickness on electron correlated compounds at the
picometer level.
