Abstract
Suspended graphene sheets exhibit correlated random deformations that can be studied under the framework of rough surfaces with a Hurst (roughness) exponent 0.72 ± 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 (SLEκ) curves with κ = 2.24 ± 0.07. 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.
Highlights
Suspended graphene sheets exhibit correlated random deformations that can be studied under the framework of rough surfaces with a Hurst exponent 0.72 ± 0.01
We have found that the distribution of the modulus of the Fourier coefficients plays an important role on this property
Since previous numerical studies have shown that the structure of graphene possesses self-affine properties[16], in this report, we show that iso-height lines, extracted at the percolation threshold, have a well-defined fractal dimension and are conformally invariant
Summary
Since previous numerical studies have shown that the structure of graphene possesses self-affine properties[16], in this report, we show that iso-height lines, extracted at the percolation threshold, have a well-defined fractal dimension and are conformally invariant This resulting height-threshold is the percolation threshold). We have imposed free boundary conditions and restricted the analysis of L × L graphene membranes to the inner
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