Ripples in graphene: A variational approach

Manuel Friedrich, Ulisse Stefanelli

Published 2018-02-14Version 1

Suspended graphene samples are observed to be gently rippled rather than being flat. In [M. Friedrich, U. Stefanelli. Graphene ground states], we have checked that this nonplanarity can be rigorously described within the classical molecular-mechanical frame of configurational-energy minimization. There, we have identified all ground-state configurations with graphene topology with respect to classes of next-to-nearest neighbor interaction energies and classified their fine nonflat geometries. In this second paper on graphene nonflatness, we refine the analysis further and prove the emergence of wave patterning. Specifically, we show that almost minimizers of the configurational energy develop waves with specific wavelength, independently of the size of the sample. This corresponds remarkably to experiments and simulations.