Thermodynamic model of twisted bilayer graphene: Entropy matters

Abstract

Twisted bilayer materials have attracted tremendous attention due to their unique and novel properties. In this work, we derive a thermodynamic model for twisted bilayer graphene (tBLG) within the framework of the classical statistical mechanics. The effect of interlayer twist is introduced by the Moiré-dependent out-of-plane deformation, based on which the twist associated Helmholtz free energy is quantified. Furthermore, the configuration entropy, reflecting the number of micro-states in Moiré unit-cells, is directly derived from both the Helmholtz free energy and the Boltzmann entropy equation with a clear physical interpretation. We show the configuration entropy of a tBLG relative to the AB-stacked bilayer graphene is proportional to the logarithmic function of the ratio of Moiré period ( a m ) and the lattice constant ( a ), i.e., S tBLG − S AB = 12 k B ln ( a m / a ) . Finally, based on the observation that the out-of-plane deformation follows the evolution of Moiré patterns, a possible dissipation mechanism in the interlayer sliding of tBLG is discussed. This work provides a theoretical guidance for studying the Moiré effect of incommensurate contact interfaces such as tribology.