  Wrinkling is a ubiquitous phenomenon in two-dimensional membranes. In
particular, in the large-scale growth of graphene on metallic substrates, high
densities of wrinkles are commonly observed. Despite their prevalence and
potential impact on large-scale graphene electronics, relatively little is
known about their structural morphology and electronic properties. Surveying
the graphene landscape using atomic force microscopy, we found that wrinkles
reach a certain maximum height before folding over. Calculations of the
energetics explain the morphological transition, and indicate that the tall
ripples are collapsed into narrow standing wrinkles by van der Waals forces,
analogous to large-diameter nanotubes. Quantum transport calculations show that
conductance through these collapsed wrinkle structures is limited mainly by a
density-of-states bottleneck and by interlayer tunneling across the collapsed
bilayer region. Also through systematic measurements across large numbers of
devices with wide folded wrinkles, we find a distinct anisotropy in their
electrical resistivity, consistent with our transport simulations. These
results highlight the coupling between morphology and electronic properties,
which has important practical implications for large-scale high-speed graphene
electronics.
