Zero sound and plasmon modes for non-Fermi liquids

Abstract

We derive the quantum Boltzmann equation (QBE) by using generalized Landau-interaction parameters, obtained through the nonequilibrium Green's function technique. This is a generalization of the usual QBE formalism to non-Fermi liquid (NFL) systems, which do not have well-defined quasiparticles. We apply this framework to a controlled low-energy effective field theory for the Ising-nematic quantum critical point, in order to find the collective excitations of the critical Fermi surface in the collisionless regime. We also compute the nature of the dispersion after the addition of weak Coulomb interactions. The zero angular momentum longitudinal vibrations of the Fermi surface show a linear-in-wavenumber dispersion, which corresponds to the zero sound of Landau's Fermi liquid theory. The Coulomb interaction modifies it to a plasmon mode in the long-wavelength limit, which disperses as the square-root of the wavenumber. Remarkably, our results show that the zero sound and plasmon modes show the same behaviour as in a Fermi liquid, although an NFL is fundamentally different from the former.

Valley-polarized nematic order in twisted moiré systems: In-plane orbital magnetism and non-Fermi liquid to Fermi liquid crossover

“…Thus, the advantage of this emergent locality in momentum space is that we can now decompose the full theory into a sum of two-patch theories, where each two-patch theory describes electronic excitations near two antipodal points, interacting with the order parameter boson with momentum along the local tangent. This formalism has been successfully used in computing the universal properties and scalings for various non-Fermi liquid systems, such as the Ising-nematic QCP [19][20][21][22][23]52], the FFLO QCP [47], and a critical Fermi surface interacting with…”