Intrinsic Negative Poisson's Ratio for Single-Layer Graphene
  Negative Poisson's ratio (NPR) materials have drawn significant interest because the enhanced toughness, shear resistance and vibration absorption that typically are seen in auxetic materials may enable a range of novel applications. In this work, we report that single-layer graphene exhibits an intrinsic NPR, which is robust and independent of its size and temperature. The NPR arises due to the interplay between two intrinsic deformation pathways (one with positive Poisson's ratio, the other with NPR), which correspond to the bond stretching and angle bending interactions in graphene. We propose an energy-based deformation pathway criteria, which predicts that the pathway with NPR has lower energy and thus becomes the dominant deformation mode when graphene is stretched by a strain above 6%, resulting in the NPR phenomenon. 
Jin-Wu Jiang, Tienchong Chang, Xingming Guo, and Harold S. Park
cond-mat.mtrl-sci