Effect of anisotropy on phase transitions in graphene

We study the effect of anisotropy (strain) on dynamical gap generation in graphene. We work with a low energy effective theory obtained from a tight-binding Hamiltonian expanded around the Dirac points in momentum space. We use a nonperturbative Schwinger-Dyson approach and calculate a coupled set of five momentum dependent dressing functions. Our results show that the critical coupling depends only weakly on the anisotropy parameter, and increases with greater anisotropy.

Figure 1

$A_2$ dressing function at different $\eta$ showing that $A_2\to 0$ as $\eta \to 1$.

Figure 2

$Z$ dressing function for different cross sections of momentum phase space.

Figure 3

$A_1$ dressing function for different cross sections of momentum phase space.

Figure 4

$A_2$ dressing function for different cross sections of momentum phase space.

Figure 5

$D$ dressing function for different cross -sections of momentum phase space.

Figure 6

$A_2$ dressing function vs angle between $p_1$ and $p_2$.

Figure 7

The renormalized Fermi velocity.

Figure 8

The condensate $D(0,0)$ vs coupling for different values of the anisotropy parameter