# Excitonic pairing of two-dimensional Dirac fermions near the antiferromagnetic quantum critical point

## TL;DR

This paper investigates how the interplay of Coulomb and short-range interactions affects excitonic pairing in 2D Dirac fermions, revealing suppression near the antiferromagnetic quantum critical point and proposing a phase diagram.

## Contribution

It introduces a comprehensive analysis of the combined effects of Coulomb and short-range interactions on excitonic pairing using Dyson-Schwinger equations, highlighting the suppression near the quantum critical point.

## Key findings

- Critical Coulomb strength increases with short-range interaction.
- Excitonic pairing is suppressed near the antiferromagnetic quantum critical point.
- A phase diagram with semimetal, excitonic insulator, and antiferromagnetic phases is proposed.

## Abstract

Two-dimensional Dirac fermions are subjected to two types of interactions, namely the long-range Coulomb interaction and the short-range on-site interaction. The former induces excitonic pairing if its strength $\alpha$ is larger than some critical value $\alpha_c$, whereas the latter drives an antiferromagnetic Mott transition when its strength $U$ exceeds a threshold $U_c$. Here, we study the impacts of the interplay of these two interactions on excitonic pairing with the Dyson-Schwinger equation approach. We find that the critical value $\alpha_c$ is increased by weak short-range interaction. As $U$ increases to approach $U_c$, the quantum fluctuation of antiferromagnetic order parameter becomes important and interacts with the Dirac fermions via the Yukawa coupling. After treating the Coulomb interaction and Yukawa coupling interaction on an equal footing, we show that $\alpha_c$ is substantially increased as $U \rightarrow U_c$. Thus, the excitonic pairing is strongly suppressed near the antiferromagnetic quantum critical point. We obtain a global phase diagram on the $U$-$\alpha$ plane, and illustrate that the excitonic insulating and antiferromagnetic phases are separated by an intermediate semimetal phase. These results provide a possible explanation of the discrepancy between recent theoretical progress on excitonic gap generation and existing experiments in suspended graphene.