Interacting Dirac Materials

TL;DR

This paper analyzes how interactions affect the Dirac spectrum in two-dimensional Dirac materials, revealing that long-range interactions increase the cone slope while short-range interactions decrease it, with implications for universal behavior.

Contribution

It provides a systematic perturbative renormalization analysis of both fermionic and bosonic Dirac quasiparticles, highlighting the effects of different interaction ranges on their spectra.

Findings

Long-range interactions increase the Dirac cone slope.

Short-range interactions decrease the Dirac cone slope.

Quasiparticle statistics influence short-range interaction effects.

Abstract

We investigate the extent to which the class of Dirac materials in two-dimensions provides general statements about the behavior of both fermionic and bosonic Dirac quasiparticles in the interacting regime. For both quasiparticle types, we find common features for the interaction induced renormalization of the conical Dirac spectrum. We perform the perturbative renormalization analysis and compute the self-energy for both quasiparticle types with different interactions and collate previous results from the literature whenever necessary. Guided by the systematic presentation of our results in Table~\ref{Summary}, we conclude that long-range interactions generically lead to an increase of the slope of the single-particle Dirac cone, whereas short-range interactions lead to a decrease. The quasiparticle statistics does not qualitatively impact the self-energy correction for long-range repulsion but does affect the behavior of short-range coupled systems, giving rise to different thermal power-law contributions. The possibility of a universal description of the Dirac materials based on these features is also mentioned.