Fate of non-Fermi liquid behavior in QED$_{3}$ at finite chemical potential

TL;DR

This paper investigates how finite chemical potential affects non-Fermi liquid behavior in 2D massless Dirac fermions coupled to gauge fields, finding that certain gauge components restore Fermi liquid behavior while others retain non-Fermi liquid characteristics.

Contribution

It provides explicit calculations of vacuum polarization functions at finite chemical potential and analyzes their impact on fermion damping rates, revealing the persistence of non-Fermi liquid behavior in some gauge components.

Findings

Temporal gauge field becomes statically screened at finite chemical potential.

Transverse gauge field remains long-ranged due to gauge invariance.

Fermion damping rate shows a non-Fermi liquid behavior ∝ ε^{2/3} at zero temperature.

Abstract

The damping rate of two-dimensional massless Dirac fermions exhibit non-Fermi liquid behavior, $\propto \epsilon^{1/2}$, due to gauge field at zero temperature and zero chemical potential. We study the fate of this behavior at finite chemical potential. We fist calculate explicitly the temporal and spatial components of vacuum polarization functions. The analytical expressions imply that the temporal component of gauge field develops a static screening length at finite chemical potential while the transverse component remains long-ranged owing to gauge invariance. We then calculate the fermion damping rate and show that the temporal gauge field leads to normal Fermi liquid behavior but the transverse gauge field leads to non-Fermi liquid behavior $\propto \epsilon^{2/3}$ at zero temperature. This energy-dependence is more regular than $\propto \epsilon^{1/2}$ and does not change as chemical potential varies.