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arXiv 1602.07597cond-mat.mtrl-scicond-mat.mes-hallphysics.comp-ph
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石墨烯片的共形不变性

Conformal Invariance of Graphene Sheets

I. Giordanelli, N. Posé, M. Mendoza, H. J. Herrmann

摘要:

悬浮的石墨烯片表现出相关的随机变形,可以在具有Hurst(粗糙度)指数$0.72 \pm 0.01$的粗糙表面的框架下进行研究。在这里,我们表明,独立的温度,在渗流阈值的等高度线有一个定义良好的分形维数和共形不变,共享相同的统计特性Schramm-Loewner演化(SLE $_κ$)曲线与$κ=2.24\pm0.07$。有趣的是,其他粗糙表面的等高线不一定是保形不变的,即使它们具有相同的赫斯特指数,例如随机高斯表面。我们已经发现,傅立叶系数的模的分布起着重要的作用,对这个属性。我们的研究结果不仅引入了一个新的普适类,并将悬浮石墨烯膜的研究置于临界现象理论中,而且还提供了关于粗糙表面等高度线共形不变性起源的长期问题的提示。

英文摘要:

Suspended graphene sheets exhibit correlated random deformations that can be studied under the framework of rough surfaces with a Hurst (roughness) exponent $0.72 \pm 0.01$. Here, we show that, independent of the temperature, the iso-height lines at the percolation threshold have a well-defined fractal dimension and are conformally invariant, sharing the same statistical properties as Schramm-Loewner evolution (SLE$_κ$) curves with $κ=2.24\pm0.07$. Interestingly, iso-height lines of other rough surfaces are not necessarily conformally invariant even if they have the same Hurst exponent, e.g. random Gaussian surfaces. We have found that the distribution of the modulus of the Fourier coefficients plays an important role on this property. Our results not only introduce a new universality class and place the study of suspended graphene membranes within the theory of critical phenomena, but also provide hints on the long-standing question about the origin of conformal invariance in iso-height lines of rough surfaces.

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