Some thermodynamical peculiarities at the Lifshitz topological transitions in trigonally warped AB-stacked bilayer graphene and graphite near K points

Similarity has been proven between the Lifshitz topological transitions (LTT) in AB-stacked trigonally warped bilayer graphene (TWBG) and graphite near K points. The density of states (DOS) has been shown to have the van Hove singularities (VHS) of type (epsilon(c) - |epsilon|)(-1/2) at LTT in AB-stacked (TWBG) and graphite near K points. The topology evolutions of the iso-energetic lines at LTT have been established, and transitions are realised via four stages. The LTT transition energy in TWBG is epsilon(c) approximate to 1 meV, while in graphite epsilon(c) approximate to 10 meV. Thermodynamical characteristics are investigated of AB-stacked TWBG and graphite near K points at LTT. Thermodynamical parameters possess of the strongest singularities at LTT near the K points: the electron specific heat C-e and compressibility delta partial derivative P/partial derivative P diverge as |z|(-1/2); and thermal coefficient of pressure delta 1/T partial derivative P/partial derivative T diverges as |z|(-3/2) (here z = mu-epsilon(c), and mu is the chemical potential). The similarity between the band structure of graphite near the K point and that of the bilayer graphene logically suggests probing of Lifshitz transitions in the advance study of both systems. The developed methodology can be used for exploration of LTT in other bilayer and multilayer structures, like hBN, silicene, germanene, etc.