二维结晶膜的绝对泊松比和弯曲刚度指数
Absolute Poisson's ratio and the bending rigidity exponent of a crystalline two-dimensional membrane
摘要：
我们计算的绝对泊松比$ν$和弯曲刚度指数$η$的一个独立的二维晶体膜嵌入到一个大的维度空间$d = 2 + d_c$，$d_c \gg 1$。我们表明，在制度的反常胡克定律，绝对泊松比的方法材料独立的值仅由空间维数$d_c$：$ν= -1 +2/d_c-a/d_c^2+\dots$其中$a\approx 1.76\pm 0.02$。此外，我们发现弯曲刚度的指数的以下表达式：$η= 2/d_c+(73-68ζ(3))/(27 d_c^2)+\dots$。这些结果不能捕获自洽筛选近似。
英文摘要：
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 $d = 2 + d_c$, $d_c \gg 1$. 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: $η= 2/d_c+(73-68ζ(3))/(27 d_c^2)+\dots$. These results cannot be captured by self-consistent screening approximation.
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