First-principles analysis of lattice thermal conductivity in monolayer and bilayer graphene

Using calculations from first principles, we investigate the lattice thermal conductivity of ideal monolayer and bilayer graphenes. Our result estimates that the intrinsic thermal conductivity of both materials is around $2200\text{W}{\text{m}}^{-1}{\text{K}}^{-1}$ at 300 K, a value close to the one observed theoretically and experimentally in graphite along the basal plane. It also illustrates the expected $T^{-1}$ dependence at higher temperatures. The little variation between monolayer and bilayer thermal conductivities suggests that the number of layers may not affect significantly the in-plane thermal properties of these systems. The intrinsic thermal conductivity also appears to be nearly isotropic for graphene.

Figure 1

(Color online) Phonon dispersion of (a) monolayer and (b) bilayer graphenes (with $A\text{−}B$ stacking) along the high-symmetry directions. Following the convention, the symbol Z denotes the out-of-plane vibration.

Figure 2

(Color online) Grüneissen parameter of (a) monolayer and (b) bilayer graphenes (with $A\text{−}B$ stacking) along the high-symmetry directions.

Figure 3

(Color online) Normalized thermal conductivity $\kappa /\tau$ along the $\Gamma \text{−}M$ direction in (a) monolayer and (b) bilayer graphenes with $A\text{−}B$ staking. The solid lines denote the combined contribution of all branches. In (b), all of the lines except the solid are doubly degenerate as the contributions of the specified branches essentially overlap.

Figure 4

(Color online) Thermal conductivity $\kappa$ along the $\Gamma \text{−}M$ direction in (a) monolayer graphene, (b) bilayer graphene with $A\text{−}B$ staking, and (c) bilayer graphene with $A\text{−}A$ staking. The dashed and the dotted lines are for the TA and the LA branches, respectively, while the solid lines denote the combined contribution $\left(\text{TA}+\text{LA}\right)$. In (b) and (c), two dotted lines (for two LA modes) essentially overlap with each other and give the false impression of one curve.