Semiconductor quantum plasmonics.

We investigate the frontier between classical and quantum plasmonics in highly doped semiconductor layers. The choice of a semiconductor platform instead of metals for our study permits an accurate description of the quantum nature of the electrons constituting the plasmonic response, which is a crucial requirement for quantum plasmonics. In particular we show that our quantum model permits to calculate the collective plasmonic resonances from the electronic states determined by an arbitrary one-dimensional potential. Furthermore, it allows us to analytically demonstrate the Lindhard formula in the limit of a vanishing confinement. Our approach is corroborated with experimental spectra in which higher order longitudinal plasmonic modes are present. This work opens the way towards the applicability of quantum engineering techniques for semiconductor plasmonics.