Absolute Poisson’s ratio and the bending rigidity exponent of a crystalline two-dimensional membrane

Abstract

We compute the absolute Poisson’s ratio ν and the bending rigidity exponent η of a free-standing two-dimensional crystalline membrane embedded into a space of large dimensionality d=2+dc, dc≫1. 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 dc: ν=−1+2∕dc−a∕dc2+… where a≈1.76±0.02. Also, we find the following expression for the exponent of the bending rigidity: η=2∕dc+(73−68ζ(3))∕(27dc2)+…. These results cannot be captured by self-consistent screening approximation.