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turn ”quantum mechanically” modify the edge twisting and warping instability. We further show that H edge saturation and SW edge reconstruction can not only improve the ’chemi- cal’ stability of graphene edges by lowering the edge energy as shown before[8, 9], but also enhance their ’mechanical’ stability by converting compressive edge stress towards tensile and hence stabilizing the planar edge structure. Our first-principles findings, which cannot be captured by classical methods, provide new insights to the understanding of mechanical stability of graphene. We suggest that experimental measurement of armchair edge ripple magnitudes for different widths and comparison with zigzag edge ripples could confirm our predictions of quantum effects in graphene edge stresses differentiating from empirical re- sults. We expect the quantum manifestation of mechanical properties such as stress to exist generally in many low-dimensional nanostructures. 

The work at Tsinghua is supported by the Ministry of Science and Technology of China 

