Using an analytically tractable kinetic model of a two-dimensional Fermi liquid of electrons, we characterize the crossovers among zero sound, first sound, and plasmons. For experimentally realized Fermi liquids in a hydrodynamic limit, both zero and first sound waves are essentially replaced by plasmons. The plasmon dispersion relation is robust against hydrodynamic effects up to acquiring the viscous-limited decay rate of a first sound wave in the hydrodynamic limit. We discuss implications for experiments in clean two-dimensional electron gases.

• Received 11 January 2018
• Revised 16 February 2018

DOI:https://doi.org/10.1103/PhysRevB.97.115449