Atypical Behavior of Collective Modes in Two-Dimensional Fermi Liquids

Since its development by L.V. Landau sixty years ago, Fermi liquid theory continues to serve as a formidable model for interacting Fermi systems in addition to providing the standard which all other models are held to. Of the numerous accomplishments of Fermi liquid theory, the calculation of various transport properties is of particular interest. In this talk we apply the Landau kinetic equation to a two-dimensional Fermi liquid and discuss the consequences of the reduced dimensionality on the behavior of the collective modes. As a function of the usual dimensionless parameter s = ω/v_F, we find expected behavior in addition to new results for the behavior of the zero sound mode c₀. Additionally, we investigate the effect of a Coulomb interaction on the system resulting in an expression for plasmon frequency ω_p in 2D with a crossover as a function of q to the zero sound mode.