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

ABSTRACT

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 $({ϵ}_c-|ϵ|{)}^{-1/2}$ 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 ϵ_c ≈ 1 meV, while in graphite ϵ_c ≈ 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 δ${\displaystyle \frac{\mathrm{\partial }P}{\mathrm{\partial }S}}$ diverge as $|z{|}^{-1/2}$; and thermal coefficient of pressure δ${\displaystyle \frac{1}{T}\frac{\mathrm{\partial }P}{\mathrm{\partial }T}}$ diverges as $|z{|}^{-3/2}$ (here z = μ–ϵ_c, and μ 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.

KEYWORDS:

• Lifshitz transitions
• graphene thermodynamic
• trigonal warping in the bilayer graphene
• electronic specific heat C_e
• thermal coefficient of pressure
• electronic compressibility

Acknowledgements

I thank Professor Peter Riseborough and the reviewers for helpful suggestions and comments. I appreciate Alistair Knot for assistance in preparation the work for submission.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data accessibility

This work includes theoretical investigations.