Absolute Poisson’s ratio and the bending rigidity exponent of a crystalline two-dimensional membrane
We compute the absolute Poisson’s ratio and the bending rigidity exponent of a free-standing two-dimensional crystalline membrane embedded into a space of large dimensionality , . We demonstrate that, in the regime of anomalous Hooke’s law, the absolute Poisson’s ratio approaches material independent value determined solely by the spatial dimensionality : where . Also, we find the following expression for the exponent of the bending rigidity: . These results cannot be captured by self-consistent screening approximation.