Universal conductance fluctuations in graphene

Universal conductance fluctuations in graphene samples at energies not very close to the Dirac point are studied analytically. We demonstrate that the conductance variance is very sensitive to the elastic scattering that breaks the valley symmetry. In the absence of such scattering (disorder potential is smooth at atomic scales and trigonal warping is negligible), the variance is four times greater than in conventional metals, which explains a recent unexpected numerical finding. Strong intravalley scattering and/or warping reduces this factor to two and only the intervalley scattering leads to same result as for conventional metals. Different universal values of the variance, when compared with experimental data, can provide important information about disorder in the system.

Figure 1

Diagrams for the conductivity correlation function $F_{\alpha \beta ,\gamma \delta }\left(\Delta ϵ,H,\Delta H\right)$ [Eq. (10)]. Gray stripes denote diffusons and Cooperons, and rendered with line blocks are Hikami boxes (see Fig. 2). The diagrams (c) and (d) with the substitution $\alpha \leftrightarrow \beta$, $\gamma \leftrightarrow \delta$, and $R\leftrightarrow A$ must also be considered.

Figure 2

[(a) and (b)] Diagrammatic representation of the integral equations for the diffuson and Cooperon. [(c) and (d)] Hikami boxes. The current vertex renormalized by disorder (dark triangle) is equal to ${\tilde{j}}_{\alpha }=2e\nu \left(1^{K{K}^{\prime }}\otimes {\tau }_{\alpha }^{AB}\right)$.