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

D. R. Saykin; I. V. Gornyi; V. Yu. Kachorovskii; I. S. Burmistrov

doi:10.1016/j.aop.2020.168108

paper

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

arXiv:2002.04554 · doi:10.1016/j.aop.2020.168108

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 $d = 2 + d_{c}$ , $d_{c} ≫ 1$ . 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 $d_{c}$ : $ν = - 1 + 2/ d_{c} - a / d_{c}^{2} + \dots$ where $a \approx 1.76 \pm 0.02$ . Also, we find the following expression for the exponent of the bending rigidity: $η = 2/ d_{c} + (73 - 68 ζ (3)) / (27 d_{c}^{2}) + \dots$ . These results cannot be captured by self-consistent screening approximation.