Plasmons, collective oscillations of conduction electrons in metals or semiconductors, can be transformed into photons and vice versa. In this way, one can manipulate light using heterostructures of nanometer size, a field known as plasmonics. In the past, these devices operated in the classical regime, where the plasmon wavelength is much larger than the Fermi wavelength of the electrons. With recent progress in experimental techniques and the fabrication of nanodevices, the quantum regime in plasmonics has been reached. A solid understanding of these plasmonic devices requires a framework to describe quantum plasmons in inhomogeneous systems. A direct computational approach to study such systems has been developed recently within the Theory of Condensed Matter department, but unfortunately, this approach is limited to relatively small setups. In this talk, I will present a novel theoretical approach for quantum plasmons in inhomogeneous media. Our method is based on the semiclassical approximation, which is formally applicable when the characteristic scale of the inhomogeneities is much larger than the wavelength of the plasmons. One of its advantages is
that it leads to semi-analytical results that do not depend on the exact shape of the inhomogeneity. I will show how we can study plasmons in both three-dimensional and two-dimensional materials with this method, and present applications to localized plasmons, plasmonic waveguides, and scattering experiments. Finally, I will sketch how we want to extend the theory to more advanced setups and discuss its possible application to specific materials by combination of the theory with first-principle electronic structure calculations, which could lead to collaborations with experimental groups within the IMM.