Coulomb interactions in systems of generalized semi-Dirac fermions

TL;DR

This paper investigates Coulomb interactions in generalized semi-Dirac fermions, revealing that interactions restore linear dispersion over a broad energy range, with implications for observable properties.

Contribution

It extends the understanding of Coulomb effects in semi-Dirac systems to arbitrary dispersion powers using renormalization group analysis.

Findings

Logarithmic divergences in self-energy are resummed.

Restoration of linear dispersion over a wide energy window.

Implications discussed for physical observables.

Abstract

Interactions have strong effects in systems with flat bands. We examine the role of Coulomb interactions in two dimensional chiral anisotropic quasiparticles that disperse linearly in one direction and have relatively flat bands near the neutrality point in the other direction, dispersing with an arbitrary positive even power law $2n\geq2$. As in the conventional semi-Dirac case $(n=1$), we show using renormalization group that strong logarithmic divergences in the self-energy of generalized semi-Dirac fermions resum and lead to a restoration of linearity in the spectrum for arbitrary $n$ over a sizable energy window in the perturbative regime. We discuss those results in light of previous non-perturbative large $N_{f}$ results and address the implications for physical observables.