Abstract

As recently explicitly demonstrated by simulation [1], the elastic
properties of pristine graphene depend on the system size as a power law.
For example, for a system of 1 cm^2, the in-plane elastic moduli are about
100 times (!) smaller while the out-of-plane elastic modulus, i.e. the
bending rigidity, is about 10000 times (!!) larger than for a system of
nanometer size. This anomalous behavior, rooted in the theory of membranes,
originates from the strong anharmonic coupling between large out-of-plane modes
and in-plane modes and should be a common feature of all 2D crystals. The strong
anharmonic coupling is in fact what stabilizes a 2D crystal (embedded in 3D
space) in relatively flat configurations, as is indeed demonstrated by their
experimental realizations.

I will discuss the consequences of the mentioned renormalization for the
response in nano-indentation of a graphene drum. I will also present some
very recent work on the scaling behavior of the elastic properties of
polycrystalline graphene.

[1] J.H. Los, A. Fasolino, and M. I. Katsnelson, Phys. Rev. Lett. 116,
015901 (2016).