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.

抽象的

已证明AB堆叠的三角形翘曲双层石墨烯（TWBG）中的Lifshitz拓扑转变（LTT）与K点附近的石墨之间存在相似性。状态密度（DOS）已证明具有van Hove奇异点（VHS）类型$（{ϵ}_C-\left|ϵ\right|{）}^{-\mathrm{1个}/\mathrm{2个}}$在AB堆叠（TWBG）中的LTT和K点附近的石墨中。已经建立了LTT等能量线的拓扑演化，并通过四个阶段实现了过渡。在TWBG的LTT跃迁能量ε _Ç  ≈1兆电子伏，而在石墨ε _Ç  ≈10兆电子伏。研究了AB堆积的TWBG和LTT处K点附近的石墨的热力学特性。热力学参数在K点附近的LTT处具有最强的奇点：电子比热C _e和可压缩性δ${\displaystyle \frac{\mathrm{\partial }P}{\mathrm{\partial }\mathrm{小号}}}$ 发散为 $|ž{|}^{-\mathrm{1个}/\mathrm{2个}}$; 和压力热系数δ${\displaystyle \frac{\mathrm{1个}}{Ť}\frac{\mathrm{\partial }P}{\mathrm{\partial }Ť}}$ 发散为 $|ž{|}^{-3/\mathrm{2个}}$（这里ž  =  μ - ε _Ç，μ是化学势）。在K点附近的石墨带结构与双层石墨烯的带结构之间的相似性从逻辑上暗示了在两个系统的高级研究中对Lifshitz跃迁的探测。所开发的方法可用于探索其他双层和多层结构中的LTT，例如hBN，硅烯，锗烯等。