Ripple induced changes in the wavefunction of graphene: An example of a fundamental symmetry breaking

Ideally, graphene may be regarded as a strictly 2-D structure. However, as it exists in a 3-D world, perturbations often distort this ideal 2-D structure. Under a variety of conditions graphene has been shown to develop ripples, which may have undesirable consequences for a variety of properties of graphene, such as electron transport. In addition to this, it has been speculated that ripples may be an intrinsic property of graphene, and it has also been suggested that unlocking the secrets of these ripples could be useful in the search for (an understanding of) the elusive Higgs boson. However, ripples in graphene can only be avoided, or utilized, if they can be reproducibly detected. Here we explore the most fundamental aspect of these ripples, that is, the effect of a static ripple structure on various properties of large graphene nanoflakes. We find that the mechanical, thermodynamic and electronic properties are unaltered by this fundamental rippling, but this spontaneous symmetry breaking induces a significant change in the structure of the wavefunction. This profound effect occurs only at the most basic level, but it should be, in principle, experimentally observable.