Effect of a Chern-Simons term on dynamical gap generation in graphene

We study the effect of a Chern-Simons term on dynamical gap generation in a low-energy effective theory that describes some features of monolayer suspended graphene. We use a nonperturbative Schwinger-Dyson approach. We solve a set of coupled integral equations for eight independent dressing functions that describe fermion and photon degrees of freedom. We find a strong suppression of the gap and corresponding increase in the critical coupling as a function of increasing Chern-Simons coefficient.

Figure 1

The ratio of the odd mass divided by the even one for solution 2 [see Eq. (45)]. The left panel shows the ratio as a function of the coupling with $\theta =0.6$, and the right panel shows the dependence on $\theta$ with $\alpha =4.0$.

Figure 2

$B_{\mathrm{even}}(0,0)$ and $B_{\mathrm{odd}}(0,0)$ as functions of the parameter $\theta$ with coupling $\alpha =4.0$.

Figure 3

$B_{\mathrm{even}}(0,p)$ as a function of momentum at fixed $\alpha =4.0$.

Figure 4

$B_{\mathrm{even}}(0,0)$ as a function of coupling for different approximations and different values of the parameter $\theta$.

Figure 5

The dressing functions $Z^{+}$ and $Z^{-}$ as functions of $p_0$, with $p$ held fixed to its maximum and minimum values, for two values of $\alpha$ and $\theta =0.6$.

Figure 6

The dressing functions $Z^{+}$ and $A^{+}$ as functions of $p$, with $p_0$ held fixed to its maximum and minimum values, for two values of $\alpha$ and $\theta =0.6$.

Figure 7

The dressing functions $Z^{+}$ and $A^{+}$ as functions of $p_0$ for $\alpha =3.4$ and $\theta \in (0,0.6)$.

Figure 8

The component ${\mathrm{\Pi }}_{00}$ as a function of $p_0$ and $p$ for $\alpha =3.4$ and $\theta \in (0,0.6)$.