ISPC «Modern information and electronic technologies» Odessa, 22 — 26 May, 2017 – 65 – PHONON DISPERSION AND SPECIFIC HEAT IN TWISTED BILAYER GRAPHENE Ph.D. Alexandr Cocemasov Moldova State University Republic of Moldova, Chisinau kocemasov@live.ru We theoretically investigated phonon dispersion and specific heat in twisted bilayer graphene with various rotation angles. It was found that rotation affects the out-of-plane acoustic phonon modes the most. It was established, that the relative difference between specific heat in bilayer graphene without twisting and twisted bilayer graphene constitutes 10—15% at 1 K and 3—6% at 5 K in dependence on rotational angle. Obtained theoretical results contribute to a better understanding of the phonon processes in graphene and are important for the design of novel heat management applications. Keywords: twisted graphene, phonons, specific heat. In recent years the interest of the physics community has been shifting toward investigation of the twisted few-layer graphene systems. When two graphene layers are placed on top of each other they can form a Moiré pattern [1, 2]. In this case, one layer is rotated relative to another layer by a specific angle. Phonon properties of twisted graphene are of fundamental scientific interest. Phonon spectrum determines a series of important physical quantities, such as sound velocities, phonon density of states, specific heat and thermal conductivity. Here, in the framework of the lattice dynamics approach, we investigate phonon properties of twisted bilayer graphene (T-BLG) with different angles of rotation θ . Schematic view of considered structure is presented in Fig. 1 (R denotes rotation axis, Γ and Κ denote two high-symmetry points). Fig. 1. Rotational scheme (a) and Brillouin zone of T-BLG with θ 21.8 = ° (b) In the case of the intralayer coupling the hexagonal symmetry of the interatomic interaction is pre- served for different θ , while in the interlayer coupling, the atomic configuration and force constant matrices are dependent on the rotational angle. For intralayer interaction we used Born – von Karman lattice dynamics approach [3] taking into consideration 4 nearest-neighbor atomic spheres. For the interlayer interactions we used the centrally-symmetric Lennard-Jones potential ( ) ( ) ( ) 12 6 () 4 ε σ/ σ/ = − Vr r r . The parameters ε = 4.6 meV and σ = 0.3276 nm reproduce the experimental values of the interlayer space and phonon dis- persion along the Γ−Α direction (perpendicular to the graphene planes) of bulk graphite. The frequencies of the shear (LA 2 , TA 2 ) and flexural (ZA 2 ) phonons are affected stronger by the twist- ing. The specific properties of these modes in T-BLG with θ 21.8 = ° (gray solid curves) and T-BLG with