Absolute Poisson's ratio and the bending rigidity exponent of a crystalline twodimensional membrane
Abstract
We compute the absolute Poisson's ratio ν and the bending rigidity exponent η of a freestanding twodimensional 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} + … where a ≈ 1 . 76 ± 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}) + … . These results cannot be captured by selfconsistent screening approximation.
 Publication:

Annals of Physics
 Pub Date:
 March 2020
 DOI:
 10.1016/j.aop.2020.168108
 arXiv:
 arXiv:2002.04554
 Bibcode:
 2020AnPhy.41468108S
 Keywords:

 Crystalline membrane;
 Tethered membrane;
 Graphene;
 Poisson's ratio;
 Condensed Matter  Mesoscale and Nanoscale Physics;
 Condensed Matter  Soft Condensed Matter;
 Condensed Matter  Statistical Mechanics
 EPrint:
 Ann. Phys. (N.Y.) 414, 168108 (2020)