  Atomically thin films, like transition metal dichalcogenides, can now be
synthesized at wafer scale, achieving the same extreme aspect ratio (~10^8)
that a sheet of paper would have if it covered an entire city. Yet, the
intrinsic (i.e. unconfined) three-dimensional shape of these extreme membranes
remains a mystery because of the very fundamentals of mechanical measurements:
to measure such an ultra-thin film, one first needs to simultaneously free it
and stabilize it without introducing confining boundaries. Here, we introduce a
counter-intuitive solution to this problem: place atomically thin films on
water. Using atomic force microscopy (AFM) and Raman spectroscopy adapted to
water's surface, we reveal that large-scale freestanding membranes
spontaneously self-wrinkle into a universal mechanical state with long emergent
length scales that follow robust scaling trends. Our analytical and numerical
models suggest that these universal trends are controlled by mesoscopic
parameters of the polycrystalline domains instead of atomistic details.
Moreover, we demonstrate experimentally that the wrinkles result in a large and
tunable reduction of elastic stiffness by up to 2 orders of magnitude. The
present work illuminates the physical properties of the world's thinnest
materials at length scales never probed before and highlights their potential
for tunable strain-controlled nanomechanical devices.
