Ab-initio energetics of graphite and multilayer graphene: stability of Bernal versus rhombohedral stacking

There has been a lot of excitement around the observation of superconductivity in twisted bilayer graphene, associated to flat bands close to the Fermi level. Such correlated electronic states also occur in multilayer rhombohedral stacked graphene (RG), which has been receiving increasing attention in the last years. In both natural and artificial samples however, multilayer stacked Bernal graphene (BG) occurs more frequently, making it desirable to determine what is their relative stability and under which conditions RG might be favored. Here, we study the energetics of BG and RG in bulk and also multilayer stacked graphene using first-principles calculations. It is shown that the electronic temperature, not accounted for in previous studies, plays a crucial role in determining which phase is preferred. We also show that the low energy states at room temperature consist of BG, RG and mixed BG-RG systems with a particular type of interface. Energies of all stacking sequences (SSs) are calculated for N = 12 layers, and an Ising model is used to fit them, which can be used for larger N as well. In this way, the ordering of low energy SSs can be determined and analyzed in terms of a few parameters. Our work clarifies inconsistent results in the literature, and sets the basis to studying the effect of external factors on the stability of multilayer graphene systems in first principles calculations.

Automated summary

This study investigates the energetics of multilayer stacked graphene using first-principles calculations, revealing the critical role of electronic temperature in determining the stability of BG and RG. Low energy states at room temperature consist of BG, RG, and mixed BG-RG systems, with Ising model analysis providing insights into the ordering of stacking sequences. This work clarifies inconsistencies in the literature and lays the foundation for studying external factors' effects on the stability of multilayer graphene systems in first principles calculations.