Conformal Invariance of Graphene Sheets

Abstract

Suspended graphene sheets exhibit correlated random deformations that can be studied under the framework of rough surfaces with a Hurst (roughness) exponent $0.72\pm 0.01$. 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${}_{\kappa }$) curves with $\kappa =2.24\pm 0.07$. 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.

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Cited by in corpus (9)

• Confining massless Dirac particles in two-dimensional curved space
• Schramm-Loewner evolution and perimeter of percolation clusters of correlated random landscapes
• Scale-invariant puddles in Graphene: Geometric properties of electron-hole distribution at the Dirac point
• The influence of statistical properties of Fourier coefficients on random surfaces
• Evidences of conformal invariance in 2d rigidity percolation
• Schramm-Loewner evolution in 2d rigidity percolation
• Scaling properties of mono-layer graphene away from the Dirac point
• Landau levels in wrinkled and rippled graphene sheets
• Conformal invariance in out-of-equilibrium Bose-Einstein condensates governed by the Gross-Pitaevskii Equation