Intrinsic ripples in graphene

Understand

The stability of two-dimensional (2D) layers and membranes is subject of a long standing theoretical debate.

• According to the so called Mermin-Wagner theorem, long wavelength fluctuations destroy the long-range order for 2D crystals.
• Similarly, 2D membranes embedded in a 3D space have a tendency to be crumpled.
• These dangerous fluctuations can, however, be suppressed by anharmonic coupling between bending and stretching modes making that a two-dimensional membrane can exist but should present strong height fluctuations.