Tunable massive and acoustic plasmons in two-dimensional plasmonic crystals

We theoretically investigate dispersion of plasma waves propagating in a lateral plasmonic crystal based on a two-dimensional electron system with grating gates. Two specific configurations are analyzed: a system with single grating gate having ungated gaps and a double-grating-gate system. We calculate the dispersion relations for the fundamental and several higher-order plasma modes, classifying them as either ${\it bright}$ or ${\it dark}$ excitations. At the boundaries of the Brillouin zones, the dispersion of both types of excitations is shown to be quadratic, justifying introduction of effective bright and dark plasmon masses. In the low-frequency limit, the plasmonic crystal spectrum exhibits an acoustic plasma mode characterized by a certain velocity. We demonstrate that the effective plasmon mass and acoustic velocity are highly sensitive to both the crystal geometry (specifically the lattice filling factor) and the gate voltages, enabling wide-range tunability.