A universal exponential factor in the dimensional crossover from graphene to graphite

Abstract

A universal exponential factor, $\gamma_{c}=\pi/2$, is disclosed for the dimensional crossover of few-layer graphene (FLG) from two-dimensional graphene to three-dimensional graphite. $\gamma_{c}$ is found by analyzing available experimental data on different properties of FLG with varying thickness. A theoretical study on the phonon spectrum of the vertical acoustic mode in FLG is carried out to further check this exponential factor $\gamma_{c}$. Interestingly, the same exponential factor appears in the dimensional crossover of the phonon mode. It turns out that the exponential factor $\gamma_{c}$ is related to the homogeneous Helmholtz-like molal equation in the mass transfer with a first order chemical reaction. The finding should provide valuable information for experimentalists and theorists in the future investigation on thickness dependent properties of FLG.