| Graphene has the ability to provide for a technological revolution. First isolated and characterized in 2004, this material shows promise in the field of flexible electronics. The electronic properties of graphene can be tuned by controlling the shape of the membrane. Of particular interest in this endeavor are the thermal ripples in graphene membranes. Years of theoretical work by such luminaries as Lev Landau, Rudolf Peierls, David Mermin and Herbert Wagner have established that 2D crystals should not be thermodynamically stable. Experimental research on thin films has supported this finding. Yet graphene exists, and freestanding graphene films have been grown on large scales. It turns out that coupling between the bending and stretching phonons can stabilize the graphene in a flat, albeit rippled phase. These ripples have attracted much attention, and recent work has shown how to arrange these ripples in a variety of configurations.;In this thesis, I will present work done using a scanning tunneling microscope (STM) to interact with freestanding graphene membranes. First I will present STM images of freestanding graphene and show how these images show signs of distortion under the electrostatic influence of the STM tip. This electrostatic attraction between the STM tip and the graphene sample can be used to pull on the graphene sample. At the same time, by employing Joule heating in order to heat graphene using the tunneling current, and exploiting the negative coefficient of thermal expansion, a repulsive thermal load can be generated.;By repeatedly pulling on the graphene using the electrostatic potential, while sequentially increasing the setpoint current we can generate a thermal mirror buckling event. Slowly heating the graphene using the tunneling current, prepares a small convex region of graphene under the tip. By increasing thermal stress, as well as pulling using the out of plane electrostatic force, the graphene suddenly and irreversibly switches the sign of its curvature. This event is discovered using STM measurements and supplemented by molecular dynamics simulations.;Finally, I will show how to characterize this transition using the famed Ising model. The ripples are modeled as individual Ising spins, which at low temperature exhibit antiferromagnetic coupling. By heating the graphene membrane, the strain increases, changing the antiferromagnetic coupling to ferromagnetic coupling, which characterizes the irreversible transition from a soft, flexible state to a rigid configuration. |
