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Intrinsic ripples with various configurations and sizes were reported to affect the physical and chemical properties of 2D materials. By performing molecular dynamics simulations and theoretical analysis, we use two geometric models of the ripple shape to explore numerically the distribution of ripples in graphene membrane. We focus on the ratio of ripple height to its diameter (t/D) which was recently shown to be the most relevant for chemical activity of graphene membranes. Our result demonstrates that the ripple density decreases as the coefficient t/D increases, in a qualitative agreement with the Boltzmann distribution derived analytically from the bending energy of the membrane. Our theoretical study provides also specific quantitative information on the ripple distribution in graphene and gives new insights applicable to other 2D materials.
The stability of two-dimensional (2D) layers and membranes is subject of a long standing theoretical debate. According to the so called Mermin-Wagner theorem, long wavelength fluctuations destroy the long-range order for 2D crystals. Similarly, 2D me
Thermal ripples of graphene are well understood at room temperature, but their quantum counterparts at low temperatures are still in need of a realistic quantitative description. Here we present atomistic path-integral Monte Carlo simulations of free
Pattern formation on semiconductor surfaces induced by low energetic ion-beam erosion under normal and oblique incidence is theoretically investigated using a continuum model in form of a stochastic, nonlocal, anisotropic Kuramoto-Sivashinsky equatio
Research on two-dimensional materials has expanded over the past two decades to become a central theme in condensed matter research today. Significant advances have been made in the synthesis and subsequent reassembly of these materials using mechani
Electronic and transport properties of Graphene, a one-atom thick crystalline material, are sensitive to the presence of atoms adsorbed on its surface. An ensemble of randomly positioned adatoms, each serving as a scattering center, leads to the Bolz