• nanomechanical and charge transport properties;
  • atomic force microscopy;
  • graphene;
  • MoS2;
  • boron nitride;
  • atomic sheets

The materials properties of graphene and other two-dimensional atomic sheets are influenced by atomic-scale defects, mechanical deformation, and microstructures. Thus, for graphene-based applications, it is essential to uncover the roles of atomic-scale defects and domain structures of two-dimensional layers in charge transport properties. This review highlights recent studies of nanomechanical and charge transport properties of two-dimensional atomic sheets, including graphene, MoS2, and boron nitrides. Because of intrinsic structural differences, two-dimensional atomic sheets give rise to unique nanomechanical properties, including a dependence on layer thickness and chemical modification that is in contrast to three-dimensional continuum media. Mapping of local conductance and nanomechanical properties on a graphene layer can be used to image the domain and microstructures of two-dimensional atomic layers. This paper also reviews recent experimental and theoretical findings on the role of bending, defects, and microstructures on nanomechanical and transport properties of graphene-derived materials.