Specific Heat of Twisted Bilayer Graphene

We have studied the phonon specific heat in single-layer, bilayer and twisted bilayer graphene. The calculations were performed using the Born-von Karman model of lattice dynamics for intralayer atomic interactions and spherically symmetric interatomic potential for interlayer interactions. We found that at temperature T<15 K, specific heat varies with temperature as T^n, where n = 1 for graphene, n = 1.6 for bilayer graphene and n = 1.3 for the twisted bilayer graphene. The phonon specific heat reveals an intriguing dependence on the twist angle in bilayer graphene, which is particularly pronounced at low temperature. The results suggest a possibility of phonon engineering of thermal properties of layered materials by twisting the atomic planes.