Influence of exchange-correlation effects on correlated electrical conductivity of triple-monolayer graphene systems

The random phase approximation (RPA), a quantum-level scheme that captures screening while neglecting exchange-correlation effects, has been widely employed to study transport properties in graphene, multilayer graphene, and N-layer graphene systems. In this work, we calculate the electrical conductivity $\sigma \left(n\right)$ of three-layer graphene systems, namely triple-monolayer graphene (3MLG) system, limited by spatially correlated charged impurity scattering, employing the RPA as well as the Hubbard approximation (HA) and the Singwi-Tosi-Land-Sjölander (STLS) scheme to respectively neglect or incorporate exchange-correlation effects. Specifically, we calculate the carrier-density-dependent conductivities of the first and second layers, ${\sigma }_1\left(n_1\right)$ and ${\sigma }_2\left(n_2\right)$, as functions of the impurity correlation length $r_0$ and the interlayer separation $d$ in a 3MLG system. The results presented in this work provide deeper insights into how exchange-correlation effects influence correlated electrical conductivity in 3MLG structures.