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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.…
Graphene is a famous realization of elastic crystalline 2D membrane. Thermal fluctuations of a 2D membrane tend to destroy the long-range order in the system. Such fluctuations are stabilized by strong anharmonicity effects, which preserve…
Graphene is the nature's thinnest elastic membrane, with exceptional mechanical and electrical properties. We report the direct observation and creation of one-dimensional (1D) and 2D periodic ripples in suspended graphene sheets, using…
One of the most exciting phenomena observed in crystalline disordered membranes, including a suspended graphene, is rippling, i.e. a formation of static flexural deformations. Despite an active research, it still remains unclear whether the…
We study the mechanism of wrinkling of suspended graphene, by means of atomistic simulations. We argue that the structural instability under edge compression is the essential physical reason for the formation of periodic ripples in…
Two-dimensional (2D) materials display nanoscale dynamic ripples that significantly impact their properties. Defects within the crystal lattice are the elementary building blocks to tailor the material's morphology. While some studies have…
Suspended graphene exhibits ripples of size ranging from 50 to 100 {\AA} and height $\sim$10{\AA}, however, their origin remains undetermined. Previous theoretical works have proposed that rippling in graphene might be generated by the…
The amount of rippling in graphene sheets is related to the interactions with the substrate or with the suspending structure. Here, we report on an irreversibility in the response to forces that act on suspended graphene sheets. This may…
Graphene is the stiffest material known so far but, due to its one-atom thickness, it is also very bendable. Consequently, free-standing graphene exhibit ripples that has major effects on its elastic properties. Here we will summarize three…
Experiments are finally revealing intricate facts about graphene which go beyond the ideal picture of relativistic Dirac fermions in pristine two dimensional (2D) space, two years after its first isolation. While observations of rippling…
Suspended graphene samples are observed to be gently rippled rather than being flat. In [M. Friedrich, U. Stefanelli. Graphene ground states, arXiv:1802.05049], we have checked that this nonplanarity can be rigorously described within the…
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…
With use of simulated friction force microscopy, we study the effect of varying temperature on the frictional properties of suspended graphene. In contrast with the theory of thermally activated friction on the surfaces of three-dimensional…
We consider a simple spin-membrane model for rippling in graphene. The model exhibits transitions from a flat but rippled membrane to a buckled one. At high temperature the transition is second order but it is first order at low temperature…
The understanding of the structural and thermal properties of membranes, low-dimensional flexible systems in a space of higher dimension, is pursued in many fields from string theory to chemistry and biology. The case of a two-dimensional…
Ever since the discovery of graphene and subsequent explosion of interest in single atom thick materials, studying their mechanical properties has been an active area of research. New length scales often necessitate a rethinking of physical…
Scanning tunneling microscopy experiments have revealed an spontaneous rippled-to-buckled transition in heated graphene sheets, in absence of any mechanical load. Several models relying on a simplified picture of the interaction between…
Graphene, dubbed as a two-dimensional material represents the topological concept of "surface" embedded in a three-dimensional space. This regard enables to employ existing theories/tools in topology to understand different…
We propose a theory of ripples in suspended graphene sheets based on two-dimensional elasticity equations that are made discrete on the honeycomb lattice and then periodized. At each point carbon atoms are coupled to Ising spins whose…
Two-dimensional materials and their mechanical properties are known to be profoundly affected by rippling deformations. However, although ripples are fairly well understood, less is known about their origin and controlled modification.…