Probing the elastic coupling at van der Waals interfaces of two-dimensional materials

The van der Waals interfaces play a crucial role in determining the physical properties and enhancing the device performances of two-dimensional materials. Here we report the investigation of the elastic coupling at the van der Waals interfaces between graphene layers and silicon oxide, via angstrom-indentation experiments combined with density functional theoretical calculations. By developing a theoretical model based on the Lennard-Jones potential, we demonstrate that the effective elastic modulus of the graphene/silicon oxide van der Waals interface is approximately 1.6 GPa, and the interlayer elastic modulus for graphene is 34.2 GPa. In addition, contact stiffness mapping of graphene with various numbers of layers on a silicon oxide substrate indicates that the very first two-dimensional (2D) layer could significantly screen the 2D--three-dimensional interface interactions.