Know the enemy: 2D Fermi liquids

TL;DR

This paper analytically investigates the validity of Fermi liquid theory in two-dimensional electron systems with Coulomb interactions, comparing it to three-dimensional systems, and maps out the phase diagram distinguishing different dynamical regimes.

Contribution

It provides a detailed analysis of the robustness of 2D Fermi liquids at high energies and temperatures, including phase diagrams and temperature corrections for effective mass.

Findings

2D Fermi liquids are robust up to high energies and temperatures similar to 3D.

The phase diagram delineates collisionless and hydrodynamic regimes in 2D and 3D.

Temperature corrections for effective mass are calculated up to third order.

Abstract

We describe an analytical theory investigating the regime of validity of the Fermi liquid theory in interacting, via the long-range Coulomb coupling, two-dimensional Fermi systems comparing it with with the corresponding 3D systems. We find that the 2D Fermi liquid theory and 2D quasiparticles are robust up to high energies and temperatures of the order of Fermi energy above the Fermi surface, very similar to the corresponding three-dimensional situation. We calculate the phase diagram in the frequency-temperature space separating the collisionless ballistic regime and the collision-dominated hydrodynamic regime for 2D and 3D interacting electron systems. We also provide the temperature corrections up to third order for the renormalized effective mass, and comment on the validity of 2D Wiedemann-Franz law and 2D Kadawoki-Woods relation.