Effect of charged impurity correlations on electrical conductivity in monolayer graphene double-layer systems

Abstract

We calculate the conductivity of graphene in three monolayer graphene double-layer structures taking into account the presence of correlations of charged impurities. We use the Boltzmann transport theory and continuum model for the structure factor S$(\mathbf {q})$ to study the electrical conductivity of monolayer graphene in presence of the second layer (bilayer graphene, monolayer graphene, or two-dimensional electron gas (2DEG)) due to the screened Coulomb scattering at T = 0 K for different values of correlation length $r_{\text {\tiny 0}}$, interlayer distance d and dielectric constant $\epsilon _{\text {\tiny 2}}, \epsilon _{\text {\tiny 3}}$, and 2DEG material parameters. We find that for considered double-layer systems, the electrical conductivity $\sigma$ increases with decreasing d for all values of $r_0$ and increases strongly (slightly) with increasing $\epsilon _2(\epsilon _3)$. We also show that $\sigma$ increases slightly (considerably) with increasing $\epsilon _3$ for $\epsilon _3 = \epsilon _{2DEG}(\epsilon _3 = \epsilon _2 = \epsilon _{2DEG})$ and the influence of correlations on $\sigma$ is negligible for low impurity concentration of layer I $n_{i1}$ ($n_{i1} \preceq$ $10^{12} {\text{ cm }}^{-2}$).

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Appendix A: The structure of supplementary material

The supplementary material to the paper consists of the following subsections:

• A The dependence of the effective interaction $W_{11}$(q) between correlated impurities and electron in layer I as a function of interlayer distance d.

• B The dependence of the resistivity of layer I as a function of the impurity density $n_{i1}$ for different values of $n_1$.

• C The dependence of the resistivity of layer I as a function of the impurity density $n_{i1}$ for different value of $\epsilon _2$.