Atypical behavior of collective modes in two-dimensional Fermi liquids.

Using the Landau kinetic equation to study the non-equilibrium behavior of interacting Fermi systems is one of the crowning achievements of Landau's Fermi liquid theory. While thorough study of transport modes has been done for standard three-dimensional Fermi liquids, an equally in-depth analysis for two dimensional Fermi liquids is lacking. In applying the Landau kinetic equation (LKE) to a two-dimensional Fermi liquid, we obtain unconventional behavior of the zero sound mode c 0. As a function of the usual dimensionless parameter s = ω/q v F, we find two peculiar results: first, for |s| > 1 we see the propagation of an undamped mode for weakly interacting systems. This differs from the three dimensional case where an undamped mode only propagates for repulsive interactions and the mode experiences Landau damping for any arbitrary attractive interaction. Second, we find that regardless of interaction strength, a propagating mode is forbidden for |s| < 1. This is profoundly different from the three-dimensional case where a mode can propagate, albeit damped. In addition, we present a revised Pomeranchuk instability condition for a two-dimensional Fermi liquid as well as equations of motion for the fluid that follow directly from the LKE. In two dimensions, we find a constant minimum for all Landau parameters for ℓ ⩾ 1 which differs from the three dimensional case. Finally we discuss the effect of a Coulomb interaction on the system resulting in the plasmon frequency ω p exhibiting a crossover to the zero sound mode.

Consequences of the inherent density dependence in one dimensional Dirac materials.

Dirac materials are systems in which the dispersion is linear in the vicinity of the Dirac points. As a consequence of this linear dispersion, the Fermi velocity is independent of density and these systems exhibit unusual behavior and possess unique physical properties that are of considerable interest. In this work we study the ground state behavior of 1D Dirac materials in two ways. First, using the Virial theorem, we find agreement with a previous result in regards to the total average ground state energy. Namely, that the total average ground state energy, regardless of dimensionality, is found to be [Formula: see text] where r s is a dimensionless constant that's a measure of density and [Formula: see text] is a constant independent of r s . As a consequence, thermodynamic results as well as the characteristic exponents of 1D Fermi systems are density independent. Second, using conventional techniques, i.e. Tomanaga-Luttinger theory, we find several unique properties that are a direct consequence of the dispersion. Specifically, the collective modes of the system exhibit electron density independence predicted from the Virial theorem. Finally, possible experimental realization of our predictions of density independent exponents are briefly discussed.