Interplanar stiffness in defect-free monocrystalline graphite

The interplanar bond strength in graphite has been identified to be very low owing to the contribution of the van der Waals interaction. However, in this study, we use microscopic picosecond ultrasound to demonstrate that the elastic constant, $C_{33}$, along the $c$ axis of defect-free monocrystalline graphite exceeds 45 GPa, which is higher than reported values by 20\%. Existing theories fail to reproduce this strongly correlated interplanar system, and our results, thus, indicate the necessity for improvement. Since the LDA+U+RPA method, including both random phase approximation correlation and short-range correlation in $p$ Wannier orbitals, shows better agreement with the observation than LDA or even than ACFDT-RPA, the experimental results indicate non-negligible electron correlation effects with respect to both the short-range and long-range interactions.