title: Atomic-Scale Variations of the Mechanical Response of 2D Materials Detected by Noncontact Atomic Force Microscopy.
abstract: We show that noncontact atomic force microscopy (AFM) is sensitive to the local stiffness in the atomic-scale limit on weakly coupled 2D materials, as graphene on metals. Our large amplitude AFM topography and dissipation images under ultrahigh vacuum and low temperature resolve the atomic and moiré patterns in graphene on Pt(111), despite its extremely low geometric corrugation. The imaging mechanisms are identified with a multiscale model based on density-functional theory calculations, where the energy cost of global and local deformations of graphene competes with short-range chemical and long-range van der Waals interactions. Atomic contrast is related with short-range tip-sample interactions, while the dissipation can be understood in terms of global deformations in the weakly coupled graphene layer. Remarkably, the observed moiré modulation is linked with the subtle variations of the local interplanar graphene-substrate interaction, opening a new route to explore the local mechanical properties of 2D materials at the atomic scale.
authors.affiliation: Departamento de Fisica de la Materia Condensada, Universidad Autónoma de Madrid, E-28049 Madrid, Spain.
authors.forename: B
authors.initials: B
authors.lastname: de la Torre
authors.affiliation: Departamento de Fisica Teorica de la Materia Condensada, Universidad Autónoma de Madrid, E-28049 Madrid, Spain.
authors.forename: M
authors.initials: M
authors.lastname: Ellner
authors.affiliation: Departamento de Fisica Teorica de la Materia Condensada, Universidad Autónoma de Madrid, E-28049 Madrid, Spain.|Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, E-28049 Madrid, Spain.
authors.forename: P
authors.initials: P
authors.lastname: Pou
authors.affiliation: Departamento de Fisica de la Materia Condensada, Universidad Autónoma de Madrid, E-28049 Madrid, Spain.|International Iberian Nanotechnology Laboratory, 4715-310 Braga, Portugal.
authors.forename: N
authors.initials: N
authors.lastname: Nicoara
authors.affiliation: Departamento de Fisica Teorica de la Materia Condensada, Universidad Autónoma de Madrid, E-28049 Madrid, Spain.|Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, E-28049 Madrid, Spain.
authors.forename: Rubén
authors.initials: R
authors.lastname: Pérez
authors.affiliation: Departamento de Fisica de la Materia Condensada, Universidad Autónoma de Madrid, E-28049 Madrid, Spain.|Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, E-28049 Madrid, Spain.|Instituto Nicolás Cabrera, Universidad Autónoma de Madrid, E-28049 Madrid, Spain.
authors.forename: J M
authors.initials: JM
authors.lastname: Gómez-Rodríguez