Role of the Lifshitz topological transitions in the thermodynamic properties of graphene.

The origin of the Lifshitz topological transition (LTT) and the 2D nature of the LTT in graphene has been established. The peculiarities of the Lifshitz topological transitions in graphene are described at the Brillouin zone centre Γ, the zone corners K in the vicinity of the Dirac points, and at the saddle point M. A general formulation of the thermodynamics at the LTT in graphene is given. The thermodynamic characteristics of graphene are investigated at the Lifshitz topological transitions. Anomalies are found in the electron specific heat , the electron thermal coefficient of pressure, and the coefficients of electron compressibility and thermal expansion in graphene at the LTT. All the thermodynamic parameters possess the strongest singularities in graphene at the LTT near the saddle points. This opens exciting opportunities for inducing and exploring the Lifshitz topological transitions in graphene.