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 - 68 ζ(3)) /(27 dc2) + … . These results cannot be captured by self-consistent 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
- E-Print:
- Ann. Phys. (N.Y.) 414, 168108 (2020)