Plasmon confinement in fractal quantum systems

Recent progress in the fabrication of materials has made it possible to create arbitrary nonperiodic two-dimensional structures in the quantum plasmon regime. This paves the way for exploring the quantum plasmomc properties of electron gases in complex geometries. In this work we study systems with a fractal dimension. We calculate the full dielectric functions of two prototypical fractals with different ramification numbers, namely the Sierpinski carpet and gasket. We show that the Sierpinski carpet has a dispersion comparable to a square lattice, but the Sierpinski gasket features highly localized plasmon modes with a flat dispersion. This strong plasmon confinement in finitely ramified fractals can provide a novel setting for manipulating light at the quantum level.