Numerical study of the conductivity of graphene monolayer within the effective field theory approach

We report on the direct numerical measurements of the conductivity of graphene monolayer. Our numerical simulations are performed in the effective lattice field theory with noncompact $3+1$-dimensional Abelian lattice gauge fields and $2+1$-dimensional staggered lattice fermions. The conductivity is obtained from the Green-Kubo relations using the maximum entropy method. We find that in a phase with spontaneously broken sublattice symmetry the conductivity rapidly decreases. For the largest value of the coupling constant used in our simulations $g=4.5$, the dc conductivity is less than the dc conductivity in the weak-coupling phase (at $g<3.5$) by at least three orders of magnitude.

Figure 1

Fermionic condensate $\langle \overline{\psi }\psi \rangle$ as a function of inverse lattice coupling constants $\beta$ at different values of mass $m$ and extrapolation to the limit $m\to 0$. Solid line is the fit of the extrapolated data with the function $\langle \overline{\psi }\psi \rangle \sim {({\beta }_c-\beta )}^{\gamma }$ with ${\beta }_c=0.0908\pm 0.0018$ and $\gamma =1.0\pm 0.16$.

Figure 2

Current-current correlators (16) for $m=0.01$. Solid lines are the fits obtained using the maximum entropy method.

Figure 3

ac conductivity $\sigma \left(w\right)$ in (17) for $m=0.01$ at $\beta$ close to ${\beta }_c$ (on the left) and at $\beta >{\beta }_c$ (on the right).

Figure 4

dc conductivity per spin per valley $\sigma \left(0\right)/4$ in units of $e^2/h$ as a function of inverse lattice coupling constants at different values of mass $m$. The result of extrapolation of the data to the limit $m\to 0$ is plotted with black dots and solid lines.

Figure 5

Linear extrapolation of the position of the second discontinuity of the dc conductivity to the limit $m\to 0$.

Figure 6

dc conductivity per spin per valley $\sigma \left(0\right)/4$ in units of $e^2/h$ as a function of inverse lattice coupling constant $\beta$ for ${20}^4$ and ${28}^4$ lattices with $m=0.01$.