Chiral symmetry restoration in monolayer graphene induced by Kekulé distortion

We propose a chiral symmetry restoration mechanism in monolayer graphene, in analogy with the strongly coupled gauge theory. The chiral (sublattice) symmetry of graphene, which is spontaneously broken under the effectively strong Coulomb interaction, is restored by introducing the Kekulé-patterned lattice distortion externally. Such a phase transition is investigated analytically using the techniques of strong-coupling expansion on the lattice gauge theory model by preserving the original honeycomb lattice structure. We discuss the relation between the chiral phase transition and the spectral gap amplitude, and we show the modification of the dispersion relation of the quasiparticles.

Figure 1

A schematic picture of the Brillouin zone corresponding to the honeycomb lattice. The Brillouin zone $\Omega$ (gray rhombic region) is spanned by the reciprocal-lattice vectors ${\mathbf{K}}_1$ and ${\mathbf{K}}_2$. If the Kekulé distortion pattern [Eq. (7)] is introduced, $\Omega$ is split into three hexagonal cells: $\tilde{\Omega }$ and ${\tilde{\Omega }}_{\pm }$, surrounding $\mathbf{k}=\mathbf{0}$ and ${\mathbf{K}}_{\pm }$ (Dirac points), respectively.

Figure 2

The free-energy per one pair of A and B sites in the strong-coupling limit, $F_{\mathrm{eff}}^{\left(0\right)}$, as a function of $\sigma$. “Honeycomb” shows $F_{\mathrm{eff}}^{\left(0\right)}\left(\sigma \right)$ in Eq. (5) with the exact form of $\Phi \left(\mathbf{k}\right)$. “Linear” shows $F_{\mathrm{eff}}^{\left(0\right)}\left(\sigma \right)$ in Eq. (5) with the linear approximation $\Phi ({\mathbf{K}}_{\pm }+\mathbf{k})\simeq (3/2)a_{{}_{\mathrm{Hc}}}(\pm k_x+i{k}_y)$. “Square” shows the effective potential obtained by the strong-coupling expansion with the square lattice formulation[9] per four square lattice sites, corresponding to a pair of honeycomb lattice sites.

Figure 3

Charge-density imbalance between two sublattices, $\sigma$, and the total energy gap $E({\mathbf{K}}_{\pm };\Delta )=\sqrt{{(v_{{}_F}\sigma /2a_{{\tau }^{\prime }})}^2+{\Delta }^2}$, as the functions of the external Kekulé distortion $\Delta$. $\sigma \left(\Delta \right)$ first grows and then decreases as $\left|\Delta \right|$ increases, vanishing at the critical value ${\Delta }_C/3h=0.485$, while $E({\mathbf{K}}_{\pm };\Delta )$ remains finite for any value of $\Delta$. The dotted line shows the gap amplitude of the free fermion.