Free-standing semiconductor nanowires in combination with advanced gate-architectures hold an exceptional promise as miniaturized building blocks in future integrated circuits. However, semiconductor nanowires are often corrupted by an increased number of close-by surface states, which are detrimental with respect to their optical and electronic properties. This conceptual challenge hampers their potentials in high-speed electronics and therefore new concepts are needed in order to enhance carrier mobilities. We have introduced a novel type of core-shell nanowire heterostructures that incorporate modulation or remote doping and hence may lead to high-mobility electrons. We demonstrate the validity of such concepts using inelastic light scattering to study single modulation-doped GaAs/Al0.16Ga0.84As core-multishell nanowires grown on silicon. We conclude from a detailed experimental study and theoretical analysis of the observed spin and charge density fluctuations that one- and two-dimensional electron channels are formed in a GaAs coaxial quantum well spatially separated from the donor ions. A total carrier density of about 3 × 10(7) cm(-1) and an electron mobility in the order of 50,000 cm(2)/(V s) are estimated. Spatial mappings of individual GaAs/Al0.16Ga0.84As core-multishell nanowires show inhomogeneous properties along the wires probably related to structural defects. The first demonstration of such unambiguous 1D- and 2D-electron channels and the respective charge carrier properties in these advanced nanowire-based quantum heterostructures is the basis for various novel nanoelectronic and photonic devices.