  We report on growth of InP-InAs core-shell nanowires and demonstration of the
formation of single quantum structures, which show Coulomb blockade effect,
over entire lengths of the nanowires. The core-shell nanowires are grown by a
selective area growth technique via metal-organic vapor phase epitaxy. The
as-grown core-shell nanowires are found to be of wurtzite crystals. The InP
cores have a hexagonal cross section, while the InAs shell are grown
preferentially on specific {1$\bar{1}$00} facets, leading to the formation of
the core-shell nanowires with an overall triangular cross section. The grown
core-shell nanowires are transferred on to a Si/SiO$_2$ substrate and then
contacted with several narrow metal electrodes. Low-temperature transport
measurements show the Coulomb-blockade effect. We analyze the measured gate
capacitance and single electron charging energy of the devices and demonstrate
that a quantum structure which shows the Coulomb blockade effect of a
many-electron quantum dot is formed over the full length of a single core-shell
nanowire and consists of the entire InAs shell in the nanowire.
