Differential Poisson's ratio of a crystalline two-dimensional membrane

Abstract

We compute the differential Poisson's ratio of a suspended two-dimensional crystalline membrane embedded into a space of large dimensionality $d\gg 1$. We demonstrate that, in the regime of anomalous Hooke's law, the differential Poisson's ratio approaches a universal value determined solely by the spatial dimensionality $d_c$, with a power-law expansion $\nu =-1/3+0.016/d_c+O(1/d_c^2)$, where $d_c=d-2$. Thus, the value $-1/3$ predicted in previous literature holds only in the limit $d_c\to \infty$.

20 pages, 3 figures

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