Absolute Poisson’s ratio and the bending rigidity exponent of a crystalline two-dimensional membrane
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 mater...
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Veröffentlicht in: | Annals of physics 2020-03, Vol.414, p.168108, Article 168108 |
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Hauptverfasser: | , , , |
Format: | Artikel |
Sprache: | eng |
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Zusammenfassung: | 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. |
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ISSN: | 0003-4916 1096-035X |
DOI: | 10.1016/j.aop.2020.168108 |