Direct Imaging, Three-dimensional Interaction Spectroscopy, and Friction Anisotropy of Atomic-scale Ripples on MoS2_{2}

Theory predicts that two-dimensional (2D) materials may only exist in the presence of out-ofplane deformations on atomic length scales, frequently referred to as ripples. While such ripples can be detected via electron microscopy, their direct observation via surface-based techniques and characterization in terms of interaction forces and energies remain limited, preventing an unambiguous study of their effect on mechanical characteristics, including but not limited to friction anisotropy. Here, we employ high-resolution atomic force microscopy to demonstrate the presence of atomic-scale ripples on supported samples of few-layer molybdenum disulfide (MoS$_{2}$). Three-dimensional force / energy spectroscopy is utilized to study the effect of ripples on the interaction landscape. Friction force microscopy reveals multiple symmetries for friction anisotropy, explained by studying rippled sample areas as a function of scan size. Our experiments contribute to the continuing development of a rigorous understanding of the nanoscale mechanics of 2D materials.Comment: 22 pages including 4 figures in the main text, 2 figures in the supplemental informatio

Inverse Layer Dependence of Friction on Chemically Doped MoS_{2}

We present the results of atomic-force-microscopy-based friction measurements on Re-doped molybdenum disulfide (MoS2). In stark contrast to the seemingly universal observation of decreasing friction with increasing number of layers on two-dimensional (2D) materials, friction on Re-doped MoS2 exhibits an anomalous, i.e. inverse dependency on the number of layers. Raman spectroscopy measurements revealed signatures of Re intercalation, leading to a decoupling between neighboring MoS2 layers and enhanced electron-phonon interactions, thus resulting in increasing friction with increasing number of layers: a new paradigm in the mechanics of 2D materials.Comment: 15 pages incl. Supplemental Material, 5 figure