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 $\alpha$ 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 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 $U\to U_c$. Thus, the excitonic pairing is strongly suppressed near the antiferromagnetic quantum critical point. We obtain a global phase diagram on the $U\text{−}\alpha$ 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.

Figure 1

The global phase diagram of a 2D Dirac fermion system on the plane spanned by Coulomb interaction parameter $\alpha$ and the on-site interaction parameter $U$. The critical line of $U_c$ is taken from Ref. [18]. The solid part of the EI critical line is plotted based on our DS equation results, and the dashed part of this line is plotted based on extrapolation.

Figure 2

Feynman diagrams of ${\mathrm{\Pi }}_c$ and ${\mathrm{\Pi }}_{\varphi }$. The difference between two diagrams lies in the expression of the vertices.

Figure 3

Diagrams of leading ($K_1$) and subleading ($K_2$) order contributions to the GN interaction kernel. Blue and red solid lines stand for fermions with spin $\sigma$ and spin $-\sigma$, respectively.

Figure 4

Feynman diagram of the fermion self-energy due to Coulomb interaction and Yukawa coupling.

Figure 5

The $\tilde{g}$ dependence of zero-momentum excitonic gap $m_0$ at $\alpha =2.2$ and $N=2$.

Figure 6

The $\alpha$ dependence of zero-momentum gap $m_0$ for different values of $v\tilde{g}$ at $N=2$.

Figure 7

The $\alpha$ dependence of $m_0$ for different values of $\lambda$ at $N=2$. Clearly, ${\alpha }_c$ is an increasing function of $\lambda$.

Figure 8

The critical line of SM-EI transition on the $\lambda \text{−}N$ plane. Here the Coulomb interaction parameter is fixed at $\alpha =3.2$.

Figure 9

The $\lambda$ dependence of ${\alpha }_c$ at a number of values of $r$. Here the fermion flavor is $N=2$.