Graphene and numerous other two-dimensional materials (2DM) possess unique mechanical, electronic and thermal properties making them ideal materials platform for variety of nanoelectromechanical sensors (NEMS), with static as well as high frequency time response [1].

Here we explore 2DM nanostructures using combination of scanning probe microscopy (SPM), ultrasonic vibrations and electrostatic interactions that reveal key nanomechanical and nanoelectromechanical properties of 2DM essential for the systems where the atomically thin layers are subjected to the flexural and normal stresses and electrical fields. We provide spatial maps of a 2DM’s buckling transition that significantly increases the sensitivity of NEMS sensors to applied stimuli, and show that it is directly linked to the local in-plane stresses in 2DM and their interaction with the substrate. Our analysis of stress in a few layer 2DM, elastically transversely isotropic material, and a complementing experimental study, indicate that stress propagation in the depth of the 2DM or it heterostructure is directly governed by the ratio of the out-of-plane Young modulus and the in-plane shear modulus. This explaining experimental observation of “ultrasonic transparency” of few layer graphene and MoS2 observed in ultrasonic force microscope (UFM) and allows to observe defects and structures under immediate surface of such materials.

We demonstrate that anisotropic properties of 2DMs allow exploration of local electrostatic interactions between the material and the substrate via nanomechanical actuation, revealing and mapping with nanoscale resolution the charges hidden under the layers of such materials [2]. By using nonlinear detection of NEMS actuation in UFM [3] we then probe actuation of 2DM with pm resolution amplitude and ps time-scale sensitivity, comparing these with the theoretical analysis.