  We investigate the ultrafast optoelectronic properties of single
Al0.3Ga0.7As/GaAs-core-shell-nanowires. The nanowires contain GaAs-based
quantum wells. For a resonant excitation of the quantum wells, we find a
picosecond photocurrent which is consistent with an ultrafast lateral expansion
of the photogenerated charge carriers. This Dember-effect does not occur for an
excitation of the GaAs-based core of the nanowires. Instead, the core exhibits
an ultrafast displacement current and a photo-thermoelectric current at the
metal Schottky contacts. Our results uncover the optoelectronic dynamics in
semiconductor core-shell nanowires comprising quantum wells, and they
demonstrate the possibility to use the low-dimensional quantum well states
therein for ultrafast photoswitches and photodetectors.
