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Conformal Invariance of Graphene Sheets
I Giordanelli1, N Posé1, M Mendoza1
1ETH Zürich, Computational Physics for Engineering Materials, IfB, Wolfgang-Pauli-Strasse 27, CH-8093 Zürich, Switzerland.
Scientific Reports
|March 11, 2016
Summary
Suspended graphene membranes exhibit fractal properties, with iso-height lines at the percolation threshold showing conformal invariance. This finding links graphene roughness to critical phenomena and Schramm-Loewner evolution (SLEκ) curves.
Area of Science:
- Physics
- Materials Science
- Statistical Mechanics
Background:
- Suspended graphene sheets display random deformations, characterized by a Hurst exponent of 0.72 ± 0.01.
- Understanding the statistical properties of these rough surfaces is crucial for materials science.
Purpose of the Study:
- To investigate the statistical properties of iso-height lines in suspended graphene membranes.
- To determine if these properties align with theories of critical phenomena and fractal geometry.
Main Methods:
- Analysis of correlated random deformations in suspended graphene sheets.
- Characterization of iso-height lines at the percolation threshold.
- Comparison with Schramm-Loewner evolution (SLEκ) curves.
Main Results:
- Iso-height lines at the percolation threshold exhibit a defined fractal dimension and conformal invariance.
- These lines share statistical properties with SLEκ curves (κ = 2.24 ± 0.07).
- The distribution of Fourier coefficients' modulus influences conformal invariance.
Conclusions:
- Suspended graphene membranes belong to a new universality class within critical phenomena theory.
- The study provides insights into the origin of conformal invariance in rough surface iso-height lines.
- Graphene membrane roughness can be modeled using concepts from statistical physics and fractal geometry.
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