相关论文: Graphene Ripples as a Realization of a Two-Dimensi…

Intrinsic ripples in freestanding graphene have been exceedingly difficult to study. Individual ripple geometry was recently imaged using scanning tunneling microscopy, but these measurements are limited to static configurations.…

In this study, we describe a new experimental approach based on constant-current scanning tunneling spectroscopy to controllably and reversibly pull freestanding graphene membranes up to 35 nm from their equilibrium height. In addition, we…

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…

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…

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…

Knowledge of and control over the curvature of ripples in freestanding graphene are desirable for fabricating and designing flexible electronic devices, and recent progress in these pursuits has been achieved using several advanced…

We study transmission in a system consisting of a curved graphene surface as an arc (ripple) of circle connected to two flat graphene sheets on the left and right sides. We introduce a mass term in the curved part and study the effect of a…

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…

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…

Systematic displacement measurements of freestanding graphene as a function of applied bias voltage and tunneling current setpoint using scanning tunneling microscopy (STM) are presented. When the bias voltage is increased the graphene…

A series of measurements using a technique called electrostatic-manipulation scanning tunneling microscopy (EM-STM) were performed on a highly-oriented pyrolytic graphite surface. The electrostatic interaction between the STM tip and the…

A technique to locally generate mechanical vibrations in freestanding graphene using scanning tunneling microscopy (STM) is presented. The frequency of the mechanical vibrations is tuned over nearly four decades and is centered around 10…

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…

We study the thermal distribution of phonons in a graphene sheet. Due to the two electronic bands there are two out-of-plane phonon modes with respect to the two sublattices. One of these modes undergoes an Ising transition by spontaneously…

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…

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 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.…