  The hydrodynamic Drude model (HDM) has been successful in describing the
optical properties of metallic nanostructures, but for semiconductors where
several different kinds of charge carriers are present, an extended theory is
required. We present a two-fluid hydrodynamic model for semiconductors
containing electrons and holes (from thermal or external excitation) or light
and heavy holes (in $p$-doped materials). The two-fluid model predicts the
existence of two longitudinal modes, an acoustic and an optical, whereas only
an optical mode is present in the HDM. By extending nonlocal Mie theory to two
plasmas, we are able to simulate the optical properties of two-fluid
nanospheres and predict that the acoustic mode gives rise to peaks in the
extinction spectra that are absent in the HDM.
