Retardation effects on plasma waves in graphene, topological insulators, and quantum wires

Retardation effects (REs) are known to cause a crossover from linear to sublinear behaviors in the dispersion relation of two-dimensional (2D) plasma waves at long wavelengths. In the present work, we systematically analyze REs on plasma waves in both 2D and 1D electron gases, and we clarify the experimental conditions for observing the crossover. We show that graphene is the only material that might gratify the conditions with current technology. Although it closely imitates graphene, the surface of 3D topological insulators is found to be unsuitable for this purpose due to strong electronic scattering by intrinsic disorder. We also show that the crossover, though theoretically possible, virtually never occurs in 1D plasma. In addition, the relevance of our results to terahertz plasmonics is discussed.