Free energy barrier and thermal-quantum behavior of sliding bilayer graphene

In multilayer graphene, the stacking order of the layers plays a crucial role in the electronic properties and the manifestation of superconductivity. By applying shear stress, it is possible to induce sliding between different layers, altering the stacking order. Here, focusing on bilayer graphene, we analyze how ionic fluctuations alter the free energy barrier between different stacking equilibria. We calculate the free energy barrier through the state-of-the-art self-consistent harmonic approximation, which can be evaluated at unstable configurations. We find that above 100 K there is a large reduction of the barrier of more than 30% due to thermal vibrations, which significantly improves the agreement between previous first-principles calculations and experiments on a single graphite crystal. As the temperature increases, the barrier remains nearly constant up to around 500 K, with a more pronounced decrease only at higher temperatures. Our approach is general and paves the way for systematically accounting for thermal effects in free energy barriers of other macroscopic systems.