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

Two-dimensional Dirac fermions are subjected to two types of interaction, 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 impact of the interplay of these two interactions on the fate of excitonic pairing by using the Dyson-Schwinger equation approach. We find that the value of $\alpha_c$ is slightly increased by weak on-site interaction. As $U$ grows to approach $U_c$, the quantum fluctuation of antiferromagnetic order parameter becomes important and interacts with Dirac fermions via the Yukawa coupling. After treating the Coulomb interaction and Yukawa coupling on equal footing, we show that $\alpha_c$ increases substantially as $U \rightarrow U_c$. Therefore, 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 the gapless 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.