相关论文: Periodic ripples in suspended graphene

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…

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…

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…

Meyer et al (2007) found that free-standing graphene sheets, just one atom thick, display spontaneous ripples. The ripples are of order 2-20 {\AA} high and 20-200 {\AA} wide. The sheets in which they appear are only one atom thick, and…

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…

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…

Understanding how the mechanical behavior of materials deviates at the nanoscale from the macroscopically established concepts is a key challenge of particular importance for graphene, given the complex interplay between its nanoscale…

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…

The nature of its intrinsic ripples is the key factor for understanding the stability of suspended graphene, and for unraveling the long-standing theoretical debate of the existence of low-dimensional crystalline state. The rippling…

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.…

We report here on a method to fabricate and characterize highly perfect, periodically rippled graphene monolayers and islands, epitaxially grown on single crystal metallic substrates under controlled UHV conditions. The periodicity of the…

We show that the interaction between flexural phonons, when corrected by the exchange of electron-hole excitations, may place the graphene sheet very close to a quantum critical point characterized by the strong suppression of the bending…

In previous studies, it proved difficult to realize periodic graphene ripples with wavelengths of few nanometers. Here we show that one-dimensional periodic graphene ripples with wavelengths from 2 nm to tens of nanometers can be…

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…

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 examine the fracture mechanics of tearing graphene. We present a molecular dynamics simulation of the propagation of cracks in clamped, free-standing graphene as a function of the out-of-plane force. The geometry is motivated by…

Graphene on a dielectric substrate exhibits spatial doping inhomogeneities, forming electron-hole puddles. Understanding and controlling the latter is of crucial importance for unraveling many of graphene's fundamental properties at 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…

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.…