Know the enemy: 2D Fermi liquids

Highlights: • Regime of validity of the Fermi liquid theory in 2D interacting Fermi systems has been investigated. • Phase diagram for hydrodynamic and ballistic regimes in the frequency–temperature space has been obtained. • Temperature correction to quasiparticle effective mass has been calculated. • 2D Wiedemann–Franz law and 2D Kadawoki–Woods relation have been discussed. 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 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.