3 research outputs found
Buckling Thin Disks and Ribbons with Non-Euclidean Metrics
I consider the problem of a thin membrane on which a metric has been
prescribed, for example by lithographically controlling the local swelling
properties of a polymer thin film. While any amount of swelling can be
accommodated locally, geometry prohibits the existence of a global strain-free
configuration. To study this geometrical frustration, I introduce a
perturbative approach. I compute the optimal shape of an annular, thin ribbon
as a function of its width. The topological constraint of closing the ribbon
determines a relationship between the mean curvature and number of wrinkles
that prevents a complete relaxation of the compression strain induced by
swelling and buckles the ribbon out of the plane. These results are then
applied to thin, buckled disks, where the expansion works surprisingly well. I
identify a critical radius above which the disk in-plane strain cannot be
relaxed completely.Comment: 6 pages, 5 figures; lengthened to clarify previously confusing
issues. To appear in EP
Graphene as an electronic membrane
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 added another dimension to the richness of the physics of graphene,
scanning single electron transistor images displayed prevalent charge
inhomogeneity. The importance of understanding these non-ideal aspects cannot
be overstated both from the fundamental research interest since graphene is a
unique arena for their interplay, and from the device applications interest
since the quality control is a key to applications. We investigate the membrane
aspect of graphene and its impact on the electronic properties. We show that
curvature generates spatially varying electrochemical potential. Further we
show that the charge inhomogeneity in turn stabilizes ripple formation.Comment: 6 pages, 11 figures. Updated version with new results about the
re-hybridization of the electronic orbitals due to rippling of the graphene
sheet. The re-hybridization adds the next-to-nearest neighbor hopping effect
discussed in the previous version. New reference to recent STM experiments
that give support to our theor
Rippling of graphene
We show that ripples observed in free-standing graphene sheets can be explained as a consequence of adsorbed OH molecules sitting on random sites. The adsorbates cause the bonds between carbon atoms to lengthen slightly. Static buckles then result from a mechanism like the one that leads to buckling of leaves. Buckles caused by roughly 20% coverage of adsorbates are consistent with experimental observations