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

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 a 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 the 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 -> 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.