Collective modes in interacting two-dimensional tomographic Fermi liquids

TL;DR

This paper introduces an analytically solvable model for 2D Fermi liquids revealing a new 'tomographic' transport regime characterized by distinct damping behaviors of parity-odd and parity-even modes, bridging collisionless and hydrodynamic regimes.

Contribution

It presents the first detailed analysis of the collisionless-tomographic-hydrodynamic crossover in 2D Fermi liquids, highlighting the role of parity-dependent relaxation rates and their impact on collective modes.

Findings

Identification of a new 'tomographic' transport regime.

Derivation of conductivity expressions across regimes.

Discovery of distinct damping behaviors for parity modes.

Abstract

We develop an analytically solvable model for interacting two-dimensional Fermi liquids with separate collisional relaxation rates for parity-odd and parity-even Fermi surface deformations. Such a disparity of collisional lifetimes exists whenever scattering is restricted to inversion-symmetric Fermi surfaces, and should thus be a generic feature of two-dimensional Fermi liquids. It implies an additional unanticipated "tomographic" transport regime (in between the standard collisionless and hydrodynamic regimes) in which even-parity modes are overdamped while odd-parity modes are collisionless. We derive expressions for both the longitudinal and the transverse conductivity and discuss the collective mode spectrum along the collisionless-tomographic-hydrodynamic crossover. Longitudinal modes cross over from zero sound in the collisionless regime to hydrodynamic first sound in the tomographic and hydrodynamic regime, where odd-parity damping appears as a subleading correction to the lifetime. In charged Fermi liquids with long-range Coulomb coupling, these modes reduce to plasmons with a strongly suppressed odd-parity correction to the damping. The transverse response, by contrast, has a specific tomographic transport regime with two imaginary odd-parity modes, one of which requires a finite repulsive interaction, distinct from both the shear sound in the collisionless regime and an overdamped diffusive current mode in the hydrodynamic limit. Our work demonstrates that there are deep many-body aspects of interacting Fermi liquids, which are often thought to be well understood theoretically, remaining unexplored.